FDA-MIMO radar target parameter estimation method based on mobile nested array

Abstract

The invention relates to an FDA-MIMO radar target parameter estimation method based on a mobile nested array, and belongs to the field of radar signal processing. The method comprises the following implementation steps: constructing a mobile nested array model of a monostatic FDA-MIMO radar, and carrying out angle and distance decoupling; a sample covariance matrix of an observation matrix is calculated, an optimization problem based on low-rank matrix reconstruction is established, a Toeplitz matrix is solved and obtained by using an alternating projection method, and a target angle and distance estimation value is obtained by using a two-dimensional subspace method. The method has the advantages that the mobile nested array is applied to FDA-MIMO, the number of virtual array elements of a differential common array is remarkably increased, the array aperture is larger, the target parameter estimation precision is higher by solving the low-rank matrix reconstruction problem, and the problems that an existing FDA-MIMO radar is low in parameter estimation precision and resolution, limited in detectable target number and the like can be solved.

Description

Technical Field

[0001] The invention belongs to the field of radar signal processing, and in particular relates to a FDA-MIMO radar target parameter estimation method based on a mobile nested array. Background Art

[0002] Multiple-input multiple-output (MIMO) radar has attracted widespread attention since its proposal. Target parameter estimation is an important research direction in MIMO radar signal processing, and has important applications in fields such as wireless positioning and tracking. However, when MIMO radar performs beam scanning, the beam pattern only depends on the angle direction and has no selectivity in the distance domain. Therefore, it cannot distinguish between two targets at the same angle but different distances.

[0003] Frequency diversity array (FDA) radar adds a frequency increment to the carrier frequency of the array element, so its beam pattern is a function related to angle, distance and time, and has the advantages of anti-clutter and anti-interference. In recent years, some scholars have combined MIMO radar and FDA radar to propose FDA-MIMO radar. This new radar can realize joint target positioning of distance and angle. Among them, joint estimation of multi-target high-resolution distance and angle parameters is one of the key issues of FDA MIMO radar. In FDAMIMO radar system, spatial resolution and the maximum number of estimable targets are related to the array aperture. If the array aperture is expanded by increasing the number of antennas, it will not only increase the cost investment, but also increase the dimension of the received signal, resulting in increased computational complexity. In recent years, the concept of sparse array has received more and more attention in the direction of arrival (DOA) estimation of array signals. Sparse array refers to an array with an array element spacing greater than half a wavelength. Commonly used sparse arrays include minimum redundant array (MRA), nested array and coprime array. It can obtain a larger virtual array aperture through array equivalence, thereby obtaining parameter estimation performance with higher resolution. The commonly used method is to convert the sparse array into an equivalent virtual uniform array based on the idea of ​​differential common array and use algorithms such as spatial smoothed MUSIC (SS-MUSIC) to achieve high-resolution DOA estimation. In order to further improve the direction finding performance of sparse arrays, some scholars have recently proposed the concept of mobile arrays in DOA estimation. It uses passive aperture technology to enable sparse arrays to utilize the mobile characteristics of the moving platform, thereby further expanding the virtual array aperture of the system. However, the current method is limited to one-dimensional DOA estimation. Summary of the invention

[0004] The invention provides a FDA-MIMO radar target parameter estimation method based on a mobile nested array to solve the problems of low accuracy and resolution and limited number of detectable targets in the existing FDA-MIMO radar parameter estimation technology.

[0005] The technical solution adopted by the present invention comprises the following steps:

[0006] Step 1: Construct a mobile nested array model of a single-base FDA-MIMO radar;

[0007] Step 2: Decouple angle and distance based on the received signal model of FDA-MIMO radar;

[0008] Step 3: Calculate the sample covariance matrix of the observation matrix X

[0009] Step 4: Based on the sample covariance matrix Establish an optimization problem based on low-rank matrix reconstruction;

[0010] Step 5: Solve the optimization problem established in step 4 using the alternating projection minimization method to obtain the Toeplitz matrix T(u);

[0011] Step 6: For the Toeplitz matrix T(u) obtained in step 5, use a two-dimensional subspace method to obtain the estimated values ​​of the target angle and distance.

[0012] The single-base FDA-MIMO radar in step 1 of the present invention comprises an M-element transmitting array and an N-element receiving array, wherein the transmitting array has an array element spacing of d t =d frequency diversity array FDA, the receiving array is array element position index Π = {Π1, Π2, ..., Π N}={nd,0≤n≤N1-1}∪{(mN1+m-1)d,1≤m≤N2}, where m and n are the mth element of the transmitting array and the nth element of the receiving array, respectively, i ,i=1,2,…,N is the position of the i-th array element of the receiving array, N1 and N2 are the nesting coefficients of the two-level nested array, satisfying N=N1+N2, d is half the wavelength, and at the same time, the receiving array moves horizontally along the linear array direction at a speed υ.

[0013] In step 2 of the present invention, it is assumed that a single-base FDA-MIMO radar receives echo signals of K targets, and after matched filtering, the received signal of the lth snapshot is It can be expressed as:

[0014]

[0015] Among them, k is the kth target among multiple targets, q k is the departure angle and arrival angle of the kth target, r k is the distance between the kth target and the array, q klis the complex reflection coefficient of the kth target in the lth snapshot, l = 1, 2, …, L, and the launch guidance vector of the kth target is where a t (q k ) is the angular steering vector of the transmitter, a tr (r k ) is the distance steering vector of the transmitter, k=1,2,…,K, △f is the frequency interval between adjacent FDA transmitting elements, c is the speed of light, (·) T represents the transpose operator, ⊙ represents the Hadamard product, and since the receiving array is a mobile nested array, the receiving steering vector of the kth target can be expressed as:

[0016] is the independent complex Gaussian noise of the lth snapshot.

[0017] In step 2 of the present invention, Perform vectorization processing, decouple the angle and distance, collect L snapshot data, and obtain the decoupled observation matrix for:

[0018]

[0019] in, To select a matrix that satisfies here Π N represents the position of the Nth element of the nested array, then the moving nested array MovingNested Array, the equivalent array of MNA is expressed as:

[0020] Π MNA ={Π1,Π2,…,Π N}∪{Π1+d,Π2+d,…,Π N +d}

[0021] P n The index value of the mth row is (m,M+Π MNA (n)-1) is 1, and the rest are all 0, Π MNA (n) represents Π MNA The nth element of , m = 1, 2, ..., M; n = 1, 2, ..., 2N; q is the angle of the target, r is the distance between the target and the array, ⊕ represents the Khatri-Rao product, is the vector f(q k ), a matrix consisting of k=1,2,…,K, To include Virtual steering vectors for all elements, represents the Kronecker product, is the vector a tr (r k ) combined matrix, is the complex reflection coefficient matrix of K targets under L snapshots, where q(l) = [q 1l ,…,q Kl ] T , the independent zero-mean complex Gaussian noise matrix is

[0022] The sample covariance matrix in step 3 of the present invention is Then the statistical covariance matrix is ​​expressed as R = E[XX H ]=PT(u)P H +σI, where E[·] is the mathematical expectation operation, It is a Toeplitz matrix based on a second-order nested matrix, with vector u as its first column element, which contains the angle and distance parameters to be estimated and the power of the target signal; σ is the noise power, and I is the unit matrix.

[0023] The sample covariance matrix in step 4 of the present invention is The following optimization problem based on low-rank matrix reconstruction is established:

[0024]

[0025] in, The error is η is a custom threshold, is the sample covariance matrix, R is the statistical covariance matrix, rank(·) is the rank operation, ||·||2 is the 2-norm of the matrix, (·) H represents the conjugate transpose operator.

[0026] In step 5 of the present invention, the equivalent problem in step 4 is expressed as:

[0027]

[0028] Among them, γ is related to η 2 Similar custom thresholds, C represents the part of the optimization problem containing the Toeplitz matrix, Indicates that there are other parts in the optimization problem;

[0029] Since T(u) has the characteristics of semi-positive definiteness, Toeplitz property and low rank, the above optimization problem is expressed as:

[0030]

[0031] Among them, R Y ={rank(Y)≤δ} is a set of low-rank matrices, and the rank of all matrices in the set is not greater than δ; is a set of semi-positive Toeplitz complex-valued matrices, the matrices Y and U belong to R Y and R U ;

[0032] In order to reduce the computational complexity of the convex optimization solution method, the following update criterion is constructed:

[0033]

[0034] in,(·) (ε) 、(·) (ε+1) They represent the result of the εth iteration and the result of the ε+1th iteration respectively. Indicates R Y The projection operator, Indicates R U The projection operator, μ1 and μ2 are the step sizes of alternating projections;

[0035] According to the above updating criteria, the alternating projection minimization problem is solved to obtain the Toeplitz matrix T(u).

[0036] In step 6 of the present invention, the Toeplitz matrix T(u) obtained in step 5 is used as a covariance matrix, and a two-dimensional subspace method is used to obtain the angle and distance estimation values ​​of the target.

[0037] The two-dimensional subspace method of the present invention adopts a two-dimensional MUSIC algorithm.

[0038] The present invention applies a sparse array such as a nested array to the FDA-MIMO receiving array, and places the nested array on a moving platform to make it mobile, converts the time gain into a spatial gain, significantly increases the number of virtual array elements of the differential common array, and has a larger array aperture compared to the traditional method. In addition, the method represents the distance-angle decoupled signal as a low-rank matrix reconstruction problem and solves it, which can realize the joint estimation of the target angle and distance, and has a higher target estimation accuracy.

[0039] The advantages of the present invention are as follows: the present invention applies the mobile nested array to the FDA-MIMO single-base radar system for the first time, and increases the maximum number of targets that can be estimated by the single-base FDA-MIMO radar system under the condition of the same number of array elements. As shown in Table 1, for a uniform linear array with M transmitting array elements and N receiving array elements, the maximum number of targets that can be estimated by the system is MN; if the receiving array is changed to a fixed second-order nested array with N array elements, where N=N1+N2, N1 and N2 are the nesting coefficients of the second-order nested array, then the maximum number of targets that can be estimated by the system is M(2N 2 -1+N); if the receiving array is changed to a mobile second-order nested array with N array elements, where N=N1+N2, N1 and N2 are the nesting coefficients of the second-order nested array, then the maximum number of estimable targets that can be estimated by the system is M(2N 2 +N).

[0040] Table 1

[0041] Array Type Fixed uniform linear array Fixed second-order nested matrix Moving second-order nested array The maximum number of targets that can be estimated MN <![CDATA[M(2N 2 -1+N)]]> <![CDATA[M(2N 2 +N)]]>

[0042] From the comparison of the maximum number of targets that can be estimated with different formations, it can be seen that the present invention applies mobile nested array expansion to the FDA-MIMO radar system, which greatly increases the maximum number of targets that can be estimated by the system; at the same time, by decoupling the angle and distance and adopting the low-rank matrix reconstruction method, the parameter estimation performance of the FDA-MIMO radar is improved; the Toeplitz covariance matrix is ​​solved by the alternating projection minimization method, which reduces the time required for convex optimization calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the FDA-MIMO radar target parameter estimation method based on mobile nested array of the present invention;

[0044] Figure 2 Schematic diagram of the transmitting array of the single-base FDA-MIMO radar system adopted by the present invention;

[0045] Figure 3 Schematic diagram of the receiving array of the single-base FDA-MIMO radar system adopted by the present invention;

[0046] Figure 4 It is a contour map of the angular distance estimation of three targets by the FDA-MIMO radar target parameter estimation method based on the mobile nested array of the present invention;

[0047] Figure 5 It is a three-dimensional spectrum of the angular distance estimation of three targets by the FDA-MIMO radar target parameter estimation method based on the mobile nested array of the present invention;

[0048] Figure 6This is a curve of the root mean square error (RMSE) of target angle estimation versus signal-to-noise ratio (SNR) when the covariance matrix reconstruction method (CMRA), spatial smoothing MUSIC method (SS-MUSIC) and the proposed method are used under the conditions of fixed nested array or mobile nested array;

[0049] Figure 7 This is the curve of the change of RMSE of target distance estimation with SNR when CMRA, SS-MUSIC and the proposed method are used respectively under the conditions of fixed nested array or mobile nested array;

[0050] Figure 8 This is a curve of the running time changing with SNR when CMRA, SS-MUSIC and the method proposed in this paper are used under the condition of mobile nested array. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is described in detail below in conjunction with specific implementation methods. Figure 1 As shown, the present invention provides a FDA-MIMO radar target parameter estimation method based on a mobile nested array, which specifically includes the following steps:

[0052] Step 1: Construct a mobile nested array model of a single-base FDA-MIMO radar;

[0053] Specifically, the specific process is as follows Figure 2 , 3 As shown, the single-base FDA-MIMO radar includes an M-element transmitting array and an N-element receiving array, where the transmitting array has an array element spacing of d t =d frequency diversity array (FDA), the receiving array is the array element position index Π = {Π1, Π2, ..., Π N}={nd,0≤n≤N1-1}∪{(mN1+m-1)d,1≤m≤N2}, where m and n are the mth element of the transmitting array and the nth element of the receiving array, respectively, i , i=1,2,…,N is the position of the i-th element of the receiving array, N1 and N2 are the nesting coefficients of the two-level nested array, satisfying N=N1+N2, d is half wavelength, and at the same time, the receiving array moves horizontally along the linear array direction at a speed υ;

[0054] Step 2: Decouple the angle and distance based on the received signal model of the FDA-MIMO radar;

[0055] Assume that a single-base FDA-MIMO radar receives echo signals from K targets. After matched filtering, the received signal of the lth snapshot is It can be expressed as:

[0056]

[0057] Among them, k is the kth target among multiple targets, q k is the departure angle and arrival angle of the kth target, r k is the distance between the kth target and the array, q kl is the complex reflection coefficient of the kth target in the lth snapshot, l = 1, 2, …, L, and the launch guidance vector of the kth target is where a t (q k ) is the angular steering vector of the transmitter, a tr (r k ) is the distance steering vector of the transmitter, k=1,2,…,K, △f is the frequency interval between adjacent FDA transmitting elements, c is the speed of light, (·) T represents the transpose operator, and ⊙ represents the Hadamard product. Since the receiving array is a moving nested array, the receiving steering vector of the kth target can be expressed as:

[0058]

[0059] is the independent complex Gaussian noise of the lth snapshot;

[0060] After matched filtering After vectorization, we get:

[0061]

[0062] in, represents the Kronecker product, vec(·) represents the vectorization operator, represents the observed signal of the lth snapshot after vectorization, represents the noise of the lth snapshot after vectorization;

[0063] In order to decouple the angle and distance information, x(l) is further expressed as:

[0064]

[0065] Where diag(·) is the operator for extracting the diagonal elements of the matrix, 1 N is an N-dimensional column vector whose values ​​are all 1;

[0066] definition To include The virtual steering vector of all information, where Π Nis the position of the Nth array element of the nested array, then the equivalent array of the mobile nested array can be expressed as Π MNA ={Π1,Π2,…,Π N}∪{Π1+d,Π2+d,…,Π N +d}, in order to decouple the angle from the distance in the signal model, the selection matrix is ​​defined in P n The index value of the mth row is (m,M+Π MNA (n)-1) is 1, and the rest are all 0, Π MNA (n) represents Π MNA The nth element of , m = 1, 2, ..., M; n = 1, 2, ..., 2N, then x(l) can be further expressed as:

[0067]

[0068] in, For Khatri-Rao, is the vector f(q k ), is the vector a tr (r k ) combination matrix, where k = 1, 2, ..., K; q(l) = [q 1l ,…,q Kl ] T It is the complex reflection coefficient vector composed of K targets in the lth snapshot. Collect the data x(l) of L snapshots and stack them, l = 1, 2, ..., L, to get the observation matrix for:

[0069]

[0070] in, is the complex reflection coefficient matrix of K targets in L snapshots, is the noise matrix;

[0071] Step 3: Calculate the sample covariance matrix of the observation matrix X

[0072] Sample covariance matrix The statistical covariance matrix is ​​then expressed as:

[0073]

[0074] Among them, R Q =E[QQ H ]=diag(ρ1,…,ρ K ) is the covariance matrix of the target reflection coefficient, ρ kis the power of the kth target, σ is the noise power, I is the unit matrix, (·) H represents the conjugate transpose operator. It is a Toeplitz matrix based on a second-order nested matrix, with vector u as its first column element. It contains the angle and distance parameters to be estimated and the power of the target signal. Its specific expression is as follows:

[0075]

[0076] T(u) has the characteristics of semi-positive definiteness, Toeplitz property and low rank;

[0077] Step 4: Sample covariance matrix obtained from step 3 The following optimization problem based on low-rank matrix reconstruction is established:

[0078]

[0079] in, The error is η is a custom threshold, rank(·) is a rank operation, ‖·||2 is the 2-norm of the matrix;

[0080] Step 5: Solve the optimization problem established in step 4 using the alternating projection minimization method to obtain the Toeplitz matrix T(u); express the equivalent problem in step 4 as:

[0081]

[0082] Among them, γ is related to η 2 Similar custom thresholds, C represents the part of the optimization problem containing the Toeplitz matrix, Indicates that there are other parts in the optimization problem;

[0083] Furthermore, since T(u) has the characteristics of semi-positive definiteness, Toeplitz property and low rank, the above optimization problem is expressed as:

[0084]

[0085] Among them, R Y ={rank(Y)≤δ} is a set of low-rank matrices, and the rank of all matrices in the set is not greater than δ; is a set of semi-positive Toeplitz complex-valued matrices. The matrices Y and U belong to R Y and R U ;

[0086] The above problem is a convex optimization problem. In order to reduce the computational complexity of the convex optimization solution method, the following update criteria are further constructed:

[0087]

[0088] in,(·) (ε) 、(·) (ε+1) They represent the result of the εth iteration and the result of the ε+1th iteration respectively. Indicates R Y The projection operator, Indicates R U The projection operator, μ1 and μ2 are the step sizes of alternating projections;

[0089] Solve the alternating projection minimization problem in step 5 according to the above update criteria, and finally obtain the Toeplitz matrix;

[0090] Step 6: Use the Toeplitz matrix T(u) obtained in step 5 as the covariance matrix, and use a two-dimensional subspace method, such as a two-dimensional MUSIC algorithm, to obtain the angle and distance estimates of the target.

[0091] The effect of the method of the present invention is further verified by the following examples through MATLAB simulation experiments.

[0092] The simulation parameters are set as follows: the FDA-MIMO radar transmitting array is a uniform linear array with the number of array elements M=7, the receiving array is a mobile nested array with the number of array elements N=4, where the two parameters of the second-order nested array are N1=2 and N2=2 respectively; and it is assumed that the array moving distance υτ=d=λ / 2, the number of targets is K=3, and the number of snapshots is set to 400.

[0093] First, in order to verify the effectiveness of the method of the present invention, Figure 4 , 5 The simulation gives the results of the angle distance estimation of three targets, among which, Figure 4 is a contour map, Figure 5 is a three-dimensional spectrum. Assume that the spatial positions of the three targets are (10°, 4Km), (40°, 4Km), (10°, 10Km), and the signal-to-noise ratio is 0dB. Figure 4 , 5 It can be concluded that the method of the present invention can achieve accurate estimation of angle and distance parameters of multiple targets. In particular, the method of the present invention can distinguish two targets with the same distance but different angles, and two targets with the same angle but different distances.

[0094] Then, in order to reflect the superiority of the method of the present invention, Figure 6 and Figure 7The root mean square error (RMSE) of angle and distance estimation using different arrays and different methods is compared. Two different receiving arrays are considered: mobile nested array and fixed nested array, and three different methods are used: the method of the present invention, the CMRA method and the SS-MUSIC method. Assuming that the spatial positions of the three targets are (-25°, 4.4Km), (35°, 5.1Km), and (0°, 5.9Km), after 100 Monte Carlo simulation experiments, the SNR changes from -10dB to 20dB with an interval of 10dB. Figure 6 is the curve of RMSE of angle estimation changing with SNR, Figure 7 is the curve of RMSE of distance estimation changing with SNR. Figure 6 and Figure 7 It can be seen that the RMSE of the angle and distance estimation of each method decreases with the increase of the signal-to-noise ratio. The RMSE of the SS-MUSIC method is the largest, followed by the CMRA method, and the RMSE of the method of the present invention is the smallest, indicating that the estimation accuracy of the method of the present invention is higher than that of the SS-MUSIC method and the CMRA method, especially when the SNR is low. In addition, under the same method, the RMSE of the mobile nested array is lower than that of the fixed nested array, indicating that the estimation accuracy of the mobile nested array is higher.

[0095] Finally, in order to verify the advantage of the method of the present invention in terms of computing speed, Figure 8 In the scenario of a single-base FDA-MIMO radar mobile nested array, the running time of the method of the present invention, the SS-MUSIC method and the CMRA method are compared. Assuming that the spatial positions of the three targets are still (-25°, 4.4Km), (35°, 5.1Km), (0°, 5.9Km), the SNR changes from -10dB to 20dB, with an interval of 10dB, and a single Monte Carlo simulation experiment is performed for each SNR. It can be seen from the result graph that the running time required by the method of the present invention is much less than that of the other two methods, and it has an advantage in computing speed.

[0096] Simulation results show that the proposed method can achieve accurate estimation of target parameters of mobile nested array FDA-MIMO radar and has better estimation performance than traditional parameter estimation methods.

Claims

1. A FDA-MIMO radar target parameter estimation method based on mobile nested array, characterized in that: The following steps are involved: Step 1: Construct a mobile nested array model of a single-base FDA-MIMO radar; Step 2: Decouple angle and distance based on the received signal model of FDA-MIMO radar; Step 3: Calculate the sample covariance matrix of the observation matrix X Step 4: Based on the sample covariance matrix Establish an optimization problem based on low-rank matrix reconstruction; Step 5: Solve the optimization problem established in step 4 using the alternating projection minimization method to obtain the Toeplitz matrix T(u); Step 6: For the Toeplitz matrix T(u) obtained in step 5, use a two-dimensional subspace method to obtain the estimated values ​​of the target angle and distance.

2. The method for estimating target parameters of a FDA-MIMO radar based on a mobile nested array according to claim 1, characterized in that: The single-base FDA-MIMO radar in step 1 includes an M-element transmitting array and an N-element receiving array, wherein the transmitting array has an array element spacing of d t =d frequency diversity array FDA, the receiving array is array element position index Π = {Π1, Π2, ..., Π N }={nd,0≤n≤N1-1}∪{(mN1+m-1)d,1≤m≤N2}, where m and n are the mth element of the transmitting array and the nth element of the receiving array, respectively, i ,i=1,2,…,N is the position of the i-th array element of the receiving array, N1 and N2 are the nesting coefficients of the two-level nested array, satisfying N=N1+N2, d is half the wavelength, and at the same time, the receiving array moves horizontally along the linear array direction at a speed υ.

3. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 1, characterized in that: In step 2, it is assumed that a single-base FDA-MIMO radar receives echo signals of K targets. After matched filtering, the received signal of the lth snapshot is It can be expressed as: Among them, k is the kth target among multiple targets, q k is the departure angle and arrival angle of the kth target, r k is the distance between the kth target and the array, q kl is the complex reflection coefficient of the kth target in the lth snapshot, l = 1, 2, …, L, and the launch guidance vector of the kth target is where a t (q k ) is the angular steering vector of the transmitter, a tr (r k ) is the distance steering vector of the transmitter, △f is the frequency interval between adjacent FDA transmitting elements, c is the speed of light, (·) T represents the transpose operator, ⊙ represents the Hadamard product, and since the receiving array is a mobile nested array, the receiving steering vector of the kth target can be expressed as: is the independent complex Gaussian noise of the lth snapshot.

4. The FDA-MIMO radar target parameter estimation method based on mobile nested array according to claim 3, characterized in that: In step 2, Perform vectorization processing, decouple the angle and distance, collect L snapshot data, and obtain the decoupled observation matrix for: in, To select a matrix that satisfies here Π N represents the position of the Nth element of the nested array, then the moving nested array MovingNested Array, the equivalent array of MNA is expressed as: P MNA ={Π1,Π2,…,Π N }∪{Π1+d,Π2+d,…,Π N +d} P n The index value of the mth row is (m,M+Π MNA (n)-1) is 1, and the rest are all 0, Π MNA (n) represents Π MNA The nth element of , m = 1, 2, ..., M; n = 1, 2, ..., 2N; q is the angle of the target, r is the distance between the target and the array, represents the Khatri-Rao product, is the vector f(q k ), a matrix consisting of k=1,2,…,K, To include Virtual steering vectors for all elements, represents the Kronecker product, is the vector a tr (r k ) combined matrix, is the complex reflection coefficient matrix of K targets under L snapshots, where q(l) = [q 1l ,…,q Kl ] T , the independent zero-mean complex Gaussian noise matrix is 5. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 1, characterized in that: The sample covariance matrix in step 3 Then the statistical covariance matrix is ​​expressed as R = E[XX H ]=PT(u)P H +σI, where E[·] is the mathematical expectation operation, It is a Toeplitz matrix based on a second-order nested matrix, with vector u as its first column element, which contains the angle and distance parameters to be estimated and the power of the target signal; σ is the noise power, and I is the unit matrix.

6. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 1, characterized in that: The sample covariance matrix in step 4 The following optimization problem based on low-rank matrix reconstruction is established: in, The error is η is a custom threshold, is the sample covariance matrix, R is the statistical covariance matrix, rank(·) is the rank operation, ||·||2 is the 2-norm of the matrix, (·) H represents the conjugate transpose operator.

7. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 1, characterized in that: In step 5, the equivalent problem in step 4 is expressed as: Among them, γ is related to η 2 Similar custom thresholds, C represents the part of the optimization problem containing the Toeplitz matrix, Indicates that there are other parts in the optimization problem; Since T(u) has the characteristics of semi-positive definiteness, Toeplitz property and low rank, the above optimization problem is expressed as: Among them, R Y ={rank(Y)≤δ} is a set of low-rank matrices, and the rank of all matrices in the set is not greater than δ; is a set of semi-positive Toeplitz complex-valued matrices, the matrices Y and U belong to R Y and R U ; In order to reduce the computational complexity of the convex optimization solution method, the following update criterion is constructed: in,(·) (ε) 、(·) (ε+1) They represent the result of the εth iteration and the result of the ε+1th iteration respectively. Indicates R Y The projection operator, Indicates R U The projection operator, μ1 and μ2 are the step sizes of alternating projections; According to the above updating criteria, the alternating projection minimization problem is solved to obtain the Toeplitz matrix T(u).

8. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 1, characterized in that: In step 6, the Toeplitz matrix T(u) obtained in step 5 is used as a covariance matrix, and a two-dimensional subspace method is used to obtain the angle and distance estimation values ​​of the target.

9. The method for estimating target parameters of FDA-MIMO radar based on mobile nested array according to claim 8, characterized in that: The two-dimensional subspace method adopts a two-dimensional MUSIC algorithm.

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