An automatic decoupling bistatic FDA-MIMO dual-mode radar positioning method

Abstract

The present invention discloses an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, comprising: down-converting and matching filtering the target echo data of the dual-mode radar, obtaining the echo data matrix received by each receiving array element and determining the final receiving signal of the dual-mode radar; calculating the covariance matrix of the received signal and obtaining the signal subspace data matrix; calculating the first signal subspace data matrix\second signal subspace data matrix of the MIMO radar mode\FDA-MIMO radar mode, and estimating the receiving angle of the target; performing column transformation on the first signal subspace data matrix\second signal subspace data matrix to obtain the first diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode, and obtaining the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode after alignment; estimating the target distance and the emission angle according to the second diagonal matrix. The present invention converts the angle distance coupling problem into a single distance calculation problem, and realizes automatic decoupling.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method. Background Art

[0002] Target positioning is an important research topic in the military and civilian fields. Phased array radar concentrates the energy of the transmitted signal at a specific angle at a single moment, which can effectively improve the performance of radar target detection. Unlike phased array radar, MIMO (Multiple-Input Multiple-Output) radar uses the spatial diversity provided by the transmitted orthogonal waveform and the combination of transmitting and receiving antennas to expand the array virtual aperture, which has the advantages of improving resolution and reducing fading. However, since both rely only on angles, their performance will be affected when there are distance-dependent targets or interference. FDA (Frequency Diverse Array) radar obtains additional distance degrees of freedom by applying a small frequency offset to the transmitting array element. Therefore, FDA can more flexibly identify target signals or interference in the multi-dimensional domain, but the distance-angle coupling term in the FDA transmission guidance vector reduces the target positioning performance of FDA radar.

[0003] Different from the single-base FDA-MIMO radar system that uses DOD (Direction of Departure) and DOA (Direction of Arrival) to solve the problem of distance angle coupling in target positioning, in the dual-base FDA-MIMO radar system, since the transmission angle of the target signal is different from the receiving angle of the target signal, the problem of distance angle coupling at the transmitting end cannot be directly solved by the receiving steering vector, which makes the distance and angle decoupling in the transmitting steering vector in the dual-base scenario more complicated.

[0004] Therefore, how to achieve distance angle decoupling in the bistatic FDA-MIMO system is the key issue in achieving target positioning in the bistatic radar system. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, comprising:

[0007] Obtaining target echo data of a dual-mode radar, wherein the target echo data of the dual-mode radar includes target echo data generated by a MIMO radar mode and target echo data generated by an FDA-MIMO radar mode;

[0008] Down-converting and matching filtering the target echo data of the dual-mode radar to obtain an echo data matrix received by each receiving array element at the receiving end, and determining the final receiving signal of the dual-mode radar according to the echo data matrix;

[0009] Calculating the covariance matrix of the final received signal of the dual-mode radar, and obtaining a signal subspace data matrix and a noise subspace data matrix after performing eigenvalue decomposition on the covariance matrix;

[0010] Based on the signal subspace theory, the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode are calculated according to the signal subspace data matrix, and the receiving angle of the target is estimated;

[0011] Performing column transformation on the first signal subspace data matrix and the second signal subspace data matrix to obtain first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, respectively, and aligning the first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode to obtain second diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, respectively;

[0012] The target distance and the emission angle are estimated according to the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode.

[0013] In one embodiment of the present invention, the transmission signal of the MIMO radar mode is:

[0014]

[0015] The transmission signal of FDA-MIMO radar mode is:

[0016]

[0017] In the formula, rect(·) represents the pulse function, T p Indicates pulse width, M 1 Indicates the number of transmitting array elements in MIMO radar mode, M 2 represents the number of transmitting array elements in the FDA-MIMO radar mode, φ 1,m' (t) represents the transmission reference signal of the transmitting array element m' in the MIMO radar mode at time t, φ 2,m (t) represents the transmission reference signal of the transmitting array element m in the FDA-MIMO radar mode at time t, f0 Indicates the signal carrier frequency, f m Indicates the frequency of the signal transmitted by the transmitting element m in the FDA-MIMO radar mode.

[0018] In one embodiment of the present invention, the final received signal of the dual-mode radar is:

[0019] x(t)=As(t)+n(t)

[0020] in,

[0021]

[0022]

[0023] In the formula, A represents the steering vector matrix, A 1 , A 2 They represent the steering vector matrices of the MIMO radar mode and the FDA-MIMO radar mode, n(t) represents Gaussian white noise, s(t) represents the transmission signal of the dual-mode radar, and f d,l represents the Doppler shift of target l in MIMO radar mode, λ 0 represents the wavelength of the transmitted signal, r l represents the propagation distance of the lth target, represents the launch angle of the lth target, θ l represents the receiving angle of the lth target, d represents the distance between the transmitting array element and the receiving array element, τ′ 0,l represents the propagation delay of the transmitted signal to the lth target, c represents the speed of light in vacuum, represents the Kronecker product, l = 1, 2, 3, ..., L, and L represents the target number.

[0024] In one embodiment of the present invention, the steps of calculating the covariance matrix of the final received signal of the dual-mode radar, and obtaining the signal subspace data matrix and the noise subspace data matrix after eigenvalue decomposition of the covariance matrix include:

[0025] Estimate the covariance matrix of the final received signal of the dual-mode radar according to the following formula:

[0026]

[0027] Where J represents the number of sampling snapshots, x(t j ) represents the t-th sample obtained by sampling x(t) j sampling snapshot data, H represents conjugate transpose;

[0028] For the covariance matrix Perform eigenvalue decomposition:

[0029]

[0030] Where U s represents the signal subspace data matrix, U n represents the noise subspace data matrix, Λ s and Λ n are all diagonal matrices consisting of eigenvalues.

[0031] In one embodiment of the present invention, based on the signal subspace theory, the steps of calculating the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode according to the signal subspace data matrix, and estimating the receiving angle of the target include:

[0032] According to the steering vector matrix A and the signal subspace data matrix U s , calculate the non-singular matrix T, where U s =AT;

[0033] The first signal subspace data matrix of the MIMO radar mode is calculated according to the following formula:

[0034] U sr1 =A r1 T

[0035] The second signal subspace data matrix of the FDA-MIMO radar mode is calculated according to the following formula:

[0036] U sr2 =A r2 T

[0037] In the formula, M is the number of transmitting array elements in MIMO radar mode 1 The number of transmitting array elements M in FDA-MIMO radar mode 2 sum;

[0038] Using the non-singular matrix T, A r1 and A r2 , estimate the receiving angle of the target.

[0039] In one embodiment of the present invention, A r2 =A r1 Φ r ;

[0040] Using the non-singular matrix T, A r1 and A r2 , the step of estimating the receiving angle of the target comprises:

[0041] Using Ar1 and A r2 , calculate the L×L dimensional diagonal matrix Φ r ,in

[0042]

[0043] Where diag represents a diagonal matrix;

[0044] Calculate Φ according to the following formula r The similarity matrix Ψ r :

[0045] Ψ=T -1 ΦT

[0046] rr

[0047] According to the following formula, Φ r The similarity matrix Ψ r Perform eigendecomposition:

[0048]

[0049] In the formula, For r The diagonal matrix consisting of the L eigenvalues ​​of for The diagonal elements in G r is the matrix composed of eigenvectors corresponding to L eigenvalues;

[0050] Estimate the receiving angle of target l according to the following formula:

[0051]

[0052] In one embodiment of the present invention, the first diagonal matrix of the MIMO radar mode is:

[0053]

[0054] The first diagonal matrix of the FDA-MIMO radar pattern is:

[0055]

[0056] The second diagonal matrix of the MIMO radar pattern is:

[0057]

[0058] In the formula,

[0059] The second diagonal matrix of the FDA-MIMO radar mode is:

[0060]

[0061] In one embodiment of the present invention, according to the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode, the target distance and the transmission angle are estimated according to the following formulas:

[0062]

[0063]

[0064] In the formula, The lth element in the second diagonal matrix representing the MIMO radar mode, Represents the lth element in the second diagonal matrix of the FDA-MIMO radar mode.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention provides an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, which uses radar receiving data in the dual mode to realize target position parameter estimation, obtains DOA estimation of the target through subarray transformation in the MIMO radar mode, then calibrates the echo data matrix containing target information in the dual radar mode, the MIMO radar mode and the FDA-MIMO radar mode using the rotation invariance of the subarray, and substitutes the DOA estimated in the MIMO radar mode into the FDA-MIMO radar mode, thereby converting the angle distance coupling problem into a single distance calculation problem, and realizing automatic decoupling.

[0067] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of the automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method provided by an embodiment of the present invention;

[0069] Figure 2 is a comparison diagram of target DOD estimation and DOA estimation root mean square error versus signal-to-noise ratio curves provided by an embodiment of the present invention;

[0070] Figure 3 It is a comparison diagram of the mean square error versus signal-to-noise ratio curves when estimating target distance provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0072] Figure 1FIG. 1 is a flow chart of an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method provided by an embodiment of the present invention. Figure 1 As shown, an embodiment of the present invention provides an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, comprising:

[0073] S1. Obtain target echo data of the dual-mode radar, where the target echo data of the dual-mode radar includes target echo data generated by the MIMO radar mode and target echo data generated by the FDA-MIMO radar mode;

[0074] S2, down-converting and matching filtering the target echo data of the dual-mode radar to obtain the echo data matrix received by each receiving array element at the receiving end, and determining the final receiving signal of the dual-mode radar according to the echo data matrix;

[0075] S3, calculating the covariance matrix of the final received signal of the dual-mode radar, and obtaining the signal subspace data matrix and the noise subspace data matrix after performing eigenvalue decomposition on the covariance matrix;

[0076] S4. Based on the signal subspace theory, the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode are calculated according to the signal subspace data matrix, and the receiving angle of the target is estimated;

[0077] S5. Perform column transformation on the first signal subspace data matrix and the second signal subspace data matrix to obtain first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, align the first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, and obtain second diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, respectively;

[0078] S6. Estimate the target distance and the transmission angle according to the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode.

[0079] In this embodiment, for the MIMO and FDA-MIMO dual-mode radar signal models, the transmission signal of the MIMO radar mode is:

[0080]

[0081] The transmission signal of FDA-MIMO radar mode is:

[0082]

[0083] In the formula, rect(·) represents the pulse function, T p Indicates pulse width, M 1Indicates the number of transmitting array elements in MIMO radar mode, M 2 represents the number of transmitting array elements in the FDA-MIMO radar mode, φ 1,m' (t) represents the transmission reference signal of the transmitting array element m' in the MIMO radar mode at time t, φ 2,m (t) represents the transmission reference signal of the transmitting array element m in the FDA-MIMO radar mode at time t, f 0 Indicates the signal carrier frequency, f m represents the frequency of the signal transmitted by the transmitting element m in the FDA-MIMO radar mode, f m =f 0 +(m-1)Δf, Δf represents the frequency deviation of the signal transmitted by each FDA-MIMO array element. Usually, Δf< <f 0 .

[0084] This embodiment considers an equidistant uniform linear array, and the spacing between the transmitting array elements and the receiving array elements in the MIMO radar mode and the FDA-MIMO radar mode are both d t =d r =d=λ max / 2,λ max is the maximum wavelength, and there is no phase ambiguity at this time. It should be understood that the target echo data of the dual-mode radar includes the target echo data generated by the MIMO radar mode and the target echo data generated by the FDA-MIMO radar mode. If there are L unrelated targets in space, DOD and DOA are Then the target echo data received by the nth receiving element from the lth target is in the form of:

[0085] y n,l =y 1,n,l +y 2,n,l (3)

[0086] In the formula, y 1,n,l Indicates that the nth receiving element in MIMO radar mode receives the target echo data of the lth target, y 2,n,l Indicates that the nth receiving element receives the target echo data of the lth target in the FDA-MIMO radar mode.

[0087] Specifically,

[0088]

[0089]

[0090] In the formula, ξ l represents the reflection coefficient of the target, τ 0 represents the propagation delay from the transmission signal of the reference array element in the transmitting array element to the target l, τ 1,m',lDenote the propagation delay of the transmitted signal from the transmitting element m' in the MIMO radar mode to the target l as τ 2,m,l Denote the propagation delay of the transmitted signal from the transmitting element m in the FDA-MIMO radar mode to the target l Denote the propagation delay of the echo signal of the target l arriving at the receiving element n as f d,l And f d,m,l Denote the Doppler frequency shifts of the target l in the MIMO radar mode and the FDA-MIMO radar mode respectively. When Δf << f, they can be considered equal

[0091] Optionally r T,l Denote the distance from the l-th target to the transmitter as r R,l Denote the distance from the l-th target to the receiver as d t Denote the spacing between the transmitting elements Denote the transmitting angle of the l-th target as θ l Denote the receiving angle of the l-th target

[0092] At the receiver, the target echo data of the dual-mode radar is down-converted and matched filtered. The target echo data received by each receiving element at the receiver is expressed as

[0093]

[0094]

[0095] Where τ 0 ′ ,l = r l / c represents the propagation delay of the transmitted signal from the reference element to the l-th target. r l = r T,l + r R,l Represents the propagation distance from the reference element to the l-th target. Since Δf is very small, the signal propagation phase difference of the FDA-MIMO radar mode and the MIMO radar mode at the l-th target can be expressed by Therefore, the target echo data received by the n-th element in the MIMO radar mode and the FDA-MIMO radar mode are respectively

[0096]

[0097]

[0098] In the formula τ 0 ′ ,l Represents the propagation delay of the signal to the l-th target, λ 0represents the wavelength of the transmitted signal, d represents the distance between the transmitting array element and the receiving array element, θ l represents the receiving angle of the lth target, r l represents the propagation distance of the lth target, represents the launch angle of the lth target, and c represents the speed of light.

[0099] Furthermore, the target echo data received by all N receiving array elements are combined to obtain the echo data matrices of the MIMO radar mode and the FDA-MIMO radar mode respectively:

[0100] x 1 =η 1 A 1 s(t) (10)

[0101] x 2 =η 2 A 2 s(t) (11)

[0102] Among them, A 1 represents the steering vector matrix of the MIMO radar mode, A 2 Represents the steering vector matrix of the FDA-MIMO radar mode.

[0103] Therefore, the final received signal of the above dual-mode radar is:

[0104]

[0105] in,

[0106]

[0107]

[0108] In the formula, A represents the steering vector matrix, A 1 , A 2 They represent the steering vector matrices of the MIMO radar mode and the FDA-MIMO radar mode, n(t) represents Gaussian white noise, s(t) represents the transmission signal of the dual-mode radar, and f d,l represents the Doppler shift of target l in MIMO radar mode, λ 0 represents the signal wavelength, r l represents the propagation distance of the lth target, d represents the distance between the transmitting array element and the receiving array element, c represents the speed of light in a vacuum, represents the Kronecker product, l = 1, 2, 3, ..., L, and L represents the target number.

[0109] In the above step S3, the steps of calculating the covariance matrix of the final received signal of the dual-mode radar, and obtaining the signal subspace data matrix and the noise subspace data matrix after performing eigenvalue decomposition on the covariance matrix include:

[0110] S301, estimate the covariance matrix of the final received signal of the dual-mode radar according to the following formula:

[0111]

[0112] Where J represents the number of sampling snapshots, x(t j ) represents the t-th sample obtained by sampling x(t) j sampling snapshot data, and H represents the conjugate transpose.

[0113] S302: the covariance matrix Perform eigenvalue decomposition:

[0114]

[0115] Where U s represents the signal subspace data matrix, U n represents the noise subspace data matrix, Λ s and Λ n are all diagonal matrices consisting of eigenvalues.

[0116] Specifically, in actual application scenarios, due to the limited number of sampling snapshots, the following formula is generally used to estimate the covariance matrix of the final received signal of the dual-mode radar:

[0117]

[0118] The data covariance matrix Performing eigenvalue decomposition yields:

[0119]

[0120] in, and Respectively represent the covariance matrix of the dual-mode radar The signal subspace data matrix and the noise subspace data matrix are composed of the eigenvectors corresponding to the L large eigenvalues ​​and the eigenvectors corresponding to the remaining MN-L small eigenvalues. and They are diagonal matrices consisting of L large eigenvalues ​​and MN-L small eigenvalues ​​respectively.

[0121] In the above step S4, based on the signal subspace theory, the step of calculating the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode according to the signal subspace data matrix, and estimating the receiving angle of the target includes:

[0122] S401, according to the steering vector matrix A and the signal subspace data matrix U s , calculate the non-singular matrix T, where U s =AT;

[0123] S402, calculating the first signal subspace data matrix of the MIMO radar mode according to the following formula:

[0124] U sr1 =A r1 T

[0125] S403, calculating the second signal subspace data matrix of the FDA-MIMO radar mode according to the following formula:

[0126] U sr2 =A r2 T

[0127] In the formula, M is the number of transmitting array elements in MIMO radar mode 1 The number of transmitting array elements M in FDA-MIMO radar mode 2 sum;

[0128] S404, using the non-singular matrix T, A r1 and A r2 , estimate the receiving angle of the target.

[0129] In this embodiment, A r2 =A r1 Φ r In the above step S404, the non-singular matrices T and A are used r1 and A r2 , the step of estimating the receiving angle of the target comprises:

[0130] Using A r1 and A r2 , calculate the L×L dimensional diagonal matrix Φ r ,in

[0131]

[0132] Where diag represents a diagonal matrix;

[0133] Calculate Φ according to the following formula r The similarity matrix Ψ r :

[0134] Ψ=T -1 ΦT

[0135] rr

[0136] According to the following formula, Φ r The similarity matrix Ψ r Perform eigendecomposition:

[0137]

[0138] In the formula, For r The diagonal matrix consisting of the L eigenvalues ​​of for The diagonal elements in G r is the matrix composed of eigenvectors corresponding to L eigenvalues;

[0139] Estimate the receiving angle of target l according to the following formula:

[0140]

[0141] Specifically, two data matrices are defined as and Expressed as:

[0142]

[0143] Among them, I represents the identity matrix and 0 represents the zero matrix.

[0144] According to subspace theory, the subspace data matrix in formula (16) can be expressed as:

[0145] U s =AT (18)

[0146] Where T represents a non-singular matrix.

[0147] Substituting formula (18) into formula (17) yields:

[0148]

[0149] in,

[0150] According to formula (19), we can get:

[0151] A r2 =A r1 Φ r (20)

[0152] Among them, Φ r Represents a diagonal matrix of L×L dimensions:

[0153]

[0154] Combining formula (19) and formula (20) we can get:

[0155]

[0156] Based on the above derivation, we can know that r and Φ r is a similarity matrix, so Φ r The diagonal elements of r The matrix eigenvalues ​​of r Performing eigenvalue decomposition yields:

[0157]

[0158] in, For r The diagonal matrix composed of the L eigenvalues ​​of G r It is the matrix consisting of the eigenvectors corresponding to the L eigenvalues.

[0159] Furthermore, the DOA of the target can be estimated as:

[0160]

[0161] According to formula (18), the relationship between the signal subspace data matrix in single mode and the signal subspace data matrix in dual mode is:

[0162]

[0163] Among them, U 1,s =A 1 T,U 1,s =A 1 T.

[0164] Therefore, the signal subspace data matrix in the MIMO radar mode can be calculated based on the signal subspace data matrix in the dual mode and expressed as:

[0165]

[0166] Here, considering the single mode η 1 is a constant and can be ignored.

[0167] Similarly, the two data matrices are defined as and

[0168]

[0169] According to the rotation invariance of the array steering vector matrix, we have:

[0170] A 1,t2 =A 1,t1 Φ 1,t (28)

[0171] in, Φ 1,t The first diagonal matrix for the MIMO radar pattern is:

[0172]

[0173] Combining formulas (25)-(29) we can get:

[0174]

[0175] In fact, the DOD of the target can be obtained by 1,t Eigenvalue decomposition is performed to estimate, but since there is no guarantee that the DOD estimated by formula (30) and the DOA estimated by formula (23) correspond to the same target, the decoupling of distance and angle in the FDA-MIMO mode cannot be guaranteed.

[0176] To this end, this embodiment uses the characteristic matrix of the received signal of the dual-mode radar to simultaneously match the signal subspace data matrix corresponding to the MIMO radar mode and the FDA-MIMO radar mode, as shown below:

[0177] According to formulas (22) and (23), it can be verified that G r and T -1 All by r The matrix of eigenvectors is composed of , so they have the following relationship:

[0178] G r =T -1 HF (31)

[0179] Where H and F represent the scale factor and column transformation matrix respectively. Substituting formulas (22) and (31) into (23), we can obtain:

[0180]

[0181] Next, we define the second diagonal matrix of the MIMO radar mode. Then, combining formulas (30) and (31), we can obtain:

[0182]

[0183] It can be seen from formula (32) and formula (33) that Φ r and Φ 1,tThe same column transformation is obtained by transforming the matrix HF column, and both are diagonal matrices, so the targets corresponding to the diagonal elements of the two must be the same. In this way, only Φ r and Φ 1,t By selecting the same diagonal index element, the DOA and DOD of the target can be estimated simultaneously.

[0184] Prior to this, the subspace data of the FDA-MIMO radar needs to be calibrated to ensure that the DOD, DOA and distance of the target signal meet a one-to-one correspondence.

[0185] Analogously to formula (26), the signal subspace in FDA-MIMO mode can be calculated as:

[0186]

[0187] Similarly, the two data matrices are defined as and

[0188]

[0189] Further deduction yields:

[0190] A 2,t2 =A 2,t1 Φ 2,t (36)

[0191] in, Φ 2,t The first diagonal matrix of the FDA-MIMO radar pattern is:

[0192]

[0193] Combining formulas (25) and (35), we can obtain:

[0194]

[0195] Obviously, Φ 2,t The diagonal elements of the matrix Ψ 2,t The eigenvalue decomposition is performed, but due to the distance angle coupling in the FDA-MIMO radar mode transmission guidance vector, that is, the distance and DOD of the target are coupled, the target distance information cannot be directly calculated. Although the corresponding DOD information in the MIMO radar mode can be estimated by formula (33) above, since it is impossible to ensure that the DOD estimation in the MIMO radar mode and the DOD estimation in the FDA-MIMO radar mode correspond to the same target, it is still impossible to solve the distance and DOD coupling problem in the FDA-MIMO radar mode by the DOD estimation in the MIMO radar mode.

[0196] To solve the above problem, this embodiment uses the received data feature matrix G in dual mode r For FDA-MIMO radar mode 2,t Specifically, the second diagonal matrix of the FDA-MIMO radar mode is first defined:

[0197]

[0198] Substituting formula (31) and (38) into the equation, we obtain:

[0199]

[0200] From formulas (32), (33) and (40), we can see that Φ r , Φ 1,t and Φ 2,t can be transformed into and Form, after calibration and The target phase information contained therein corresponds one to one. At this time, the target DOD estimation obtained by the MIMO radar can be used to solve the target DOD and distance coupling problem in the FDA-MIMO radar.

[0201] The FDA-MIMO radar mode implements a two-dimensional range-angle dependent transmission beam pattern by applying a small frequency offset Δf between array elements. In order to ensure the performance of target distance estimation, the target distance range is usually constrained to At this time, the FDA-MIMO radar mode has a transmission steering vector of 2πΔfr l / c item satisfies 0<2πΔfr l / c<2π.

[0202] Based on the above analysis, the diagonal elements of the matrices in each mode after calibration correspond to the same target. Therefore, the phase term related to the target distance in the FDA-MIMO radar mode can be obtained by the second diagonal matrix and Therefore, for the lth target, the phase term related to the target distance in the transmitting steering vector in the FDA-MIMO radar mode can be expressed as:

[0203]

[0204] in, and They are the second diagonal matrix in MIMO radar mode respectively It is easy to verify that when When k=0; when When k=1. Therefore, the distance to the target can be calculated as:

[0205]

[0206] Finally, the DOD estimate of the target can be obtained by the target estimated distance r l It is expressed as:

[0207]

[0208] In summary, the DOA, distance, and DOD of the lth target in the FDA-MIMO mode are estimated as follows:

[0209]

[0210] Next, the automatic decoupling dual-base FDA-MIIMO dual-mode radar positioning method provided by the present invention is further described in conjunction with simulation experiments.

[0211] In this embodiment, the transmitting end and the receiving end of the dual-mode radar system are uniform linear arrays, and the spacing between the transmitting array elements and the receiving array elements is The remaining simulation parameters are shown in Table 1:

[0212] Table 1

[0213]

[0214] Figure 2 : is a comparison diagram of the target DOD estimation and DOA estimation root mean square error versus signal-to-noise ratio curve provided by an embodiment of the present invention. Figure 2 As shown, in the target DOA estimation, the mean square error curve of the automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method provided by the present invention is basically consistent with or even slightly lower than the mean square error curves of the other two existing methods, indicating that this method can obtain better performance in target DOA estimation. In the DOD estimation of the target, due to the use of the FDA-MIMO mode, the DOD of the target is coupled with the distance, so compared with the two existing methods, the DOD estimation performance of the automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method provided by the present invention is slightly inferior. However, considering that this method avoids the spectrum peak search and complex array design and corresponding multi-parameter pairing problems involved in target estimation, such a compromise in performance is reasonable.

[0215] Figure 3 : is a comparison chart of the mean square error and signal-to-noise ratio variation curves of target distance estimation provided by an embodiment of the present invention. Figure 3As shown, no matter what the target input signal-to-noise ratio is, the automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method provided by the present invention is smaller than the distance mean square error of the other two existing methods, indicating that this method can obtain better performance when estimating the target distance. In summary, it can be seen that the automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method can effectively realize the target positioning function in the dual-base FDA-MIMO mode.

[0216] It can be seen from the above embodiments that the beneficial effects of the present invention are:

[0217] The present invention provides an automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, which uses radar receiving data in the dual mode to realize target position parameter estimation, obtains DOA estimation of the target through subarray transformation in the MIMO radar mode, then calibrates the echo data matrix containing target information in the dual radar mode, the MIMO radar mode and the FDA-MIMO radar mode using the rotation invariance of the subarray, and substitutes the DOA estimated in the MIMO radar mode into the FDA-MIMO radar mode, thereby converting the angle distance coupling problem into a single distance calculation problem, and realizing automatic decoupling.

[0218] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0219] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification.

[0220] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the present application for which protection is sought, a person skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims.

[0221] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. An automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method, It is characterized in that include: Obtaining target echo data of a dual-mode radar, wherein the target echo data of the dual-mode radar includes target echo data generated by a MIMO radar mode and target echo data generated by an FDA-MIMO radar mode; Down-converting and matching filtering the target echo data of the dual-mode radar to obtain an echo data matrix received by each receiving array element at the receiving end, and determining the final receiving signal of the dual-mode radar according to the echo data matrix; Calculating the covariance matrix of the final received signal of the dual-mode radar, and obtaining a signal subspace data matrix and a noise subspace data matrix after performing eigenvalue decomposition on the covariance matrix; Based on the signal subspace theory, the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode are calculated according to the signal subspace data matrix, and the receiving angle of the target is estimated; Performing column transformation on the first signal subspace data matrix and the second signal subspace data matrix to obtain first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, respectively, and aligning the first diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode to obtain second diagonal matrices of the MIMO radar mode and the FDA-MIMO radar mode, respectively; The target distance is estimated according to the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode, and the emission angle of the target is estimated according to the target distance.

2. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 1, It is characterized in that The transmitted signal of MIMO radar mode is: The transmission signal of FDA-MIMO radar mode is: In the formula, rect(·) represents the pulse function, T p Indicates pulse width, M 1 Indicates the number of transmitting array elements in MIMO radar mode, M 2 represents the number of transmitting array elements in the FDA-MIMO radar mode, φ 1,m' (t) represents the transmission reference signal of the transmitting array element m' in the MIMO radar mode at time t, φ 2,m (t) represents the transmission reference signal of the transmitting array element m in the FDA-MIMO radar mode at time t, f 0 Indicates the signal carrier frequency, f m Indicates the frequency of the signal transmitted by the transmitting element m in the FDA-MIMO radar mode.

3. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 2, It is characterized in that The final received signal of the dual-mode radar is: x(t)=As(t)+n(t) in, In the formula, A represents the steering vector matrix, A 1 , A 2 They represent the steering vector matrices of the MIMO radar mode and the FDA-MIMO radar mode, n(t) represents Gaussian white noise, s(t) represents the transmission signal of the dual-mode radar, and f d,l represents the Doppler shift of target l in MIMO radar mode, λ 0 represents the wavelength of the transmitted signal, r l represents the propagation distance of the lth target, represents the launch angle of the lth target, θ l represents the receiving angle of the lth target, d represents the distance between the transmitting array element and the receiving array element, τ′ 0,l represents the propagation delay of the signal to the lth target, c represents the speed of light in vacuum, represents the Kronecker product, l = 1, 2, 3…, L, and L represents the target number.

4. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 3, It is characterized in that The steps of calculating the covariance matrix of the final received signal of the dual-mode radar and obtaining the signal subspace data matrix and the noise subspace data matrix after performing eigenvalue decomposition on the covariance matrix include: Estimate the covariance matrix of the final received signal of the dual-mode radar according to the following formula: Where J represents the number of sampling snapshots, x(t j ) represents the t-th sample obtained by sampling x(t) j sampling snapshot data, H represents conjugate transpose; For the covariance matrix Perform eigenvalue decomposition: Where U s represents the signal subspace data matrix, U n represents the noise subspace data matrix, Λ s and Λ n are all diagonal matrices consisting of eigenvalues.

5. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 4, It is characterized in that Based on the signal subspace theory, the steps of calculating the first signal subspace data matrix of the MIMO radar mode and the second signal subspace data matrix of the FDA-MIMO radar mode according to the signal subspace data matrix, and estimating the receiving angle of the target include: According to the steering vector matrix A and the signal subspace data matrix U s , calculate the non-singular matrix T, where U s =AT; The first signal subspace data matrix of the MIMO radar mode is calculated according to the following formula: U sr1 =A r1 T The second signal subspace data matrix of the FDA-MIMO radar mode is calculated according to the following formula: U sr2 =A r2 T In the formula, M is the number of transmitting array elements in MIMO radar mode 1 The number of transmitting array elements M in FDA-MIMO radar mode 2 sum; Using the non-singular matrix T, A r1 and A r2 , estimate the receiving angle of the target.

6. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 5, It is characterized in that A r2 =A r1 F r ; Using the non-singular matrix T, A r1 and A r2 , the step of estimating the receiving angle of the target, include: Using A r1 and A r2 , calculate the L×L dimensional diagonal matrix Φ r ,in Where diag represents a diagonal matrix; Calculate Φ according to the following formula r The similarity matrix Ψ r : P r =T -1 F r T According to the following formula, Φ r The similarity matrix Ψ r Perform eigendecomposition: In the formula, For r The diagonal matrix consisting of the L eigenvalues ​​of for The diagonal elements in G r is the matrix composed of eigenvectors corresponding to L eigenvalues; Estimate the receiving angle of target l according to the following formula:

7. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 6, It is characterized in that The first diagonal matrix of the MIMO radar pattern is: The first diagonal matrix of the FDA-MIMO radar pattern is: The second diagonal matrix of the MIMO radar pattern is: In the formula, The second diagonal matrix of the FDA-MIMO radar mode is:

8. The automatic decoupling dual-base FDA-MIMO dual-mode radar positioning method according to claim 7, It is characterized in that According to the second diagonal matrix of the MIMO radar mode and the FDA-MIMO radar mode, the target distance and the emission angle are estimated according to the following formulas: In the formula, The lth element in the second diagonal matrix representing the MIMO radar mode, The lth element in the second diagonal matrix representing the FDA-MIMO radar mode, Indicates the target distance, represents the transmission angle, and Δf represents the frequency offset.

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