An FDA-MIMO radar incremental range-angle joint estimation method

Abstract

The present application relates to a kind of FDA-MIMO radar incremental distance-angle joint estimation method, comprising the following steps: using the echo data of FDA-MIMO radar to establish the signal model of incremental distance and angle;Incremental distance information and angle information in signal model are separated, and the decoupling model of FDA-MIMO radar incremental distance and angle is established;Based on decoupling model, define the two-dimensional atom norm of FDA-MIMO radar target incremental distance and angle, the minimum problem of two-dimensional atom norm is converted into the first semi-positive programming problem, and the first semi-positive programming problem is used as parameter estimation function;Based on parameter estimation function, the incremental distance estimation value and angle estimation value of target are calculated.The method can directly estimate the incremental distance estimation value and angle of target in continuous domain, the method does not need to carry out grid division to space domain, can solve grid mismatch problem, effectively improve the precision of parameter estimation result, improve the efficiency of parameter estimation.

Description

Technical Field

[0001] This invention belongs to the field of radar target parameter estimation, specifically involving an FDA-MIMO radar incremental range-angle joint estimation method. Background Technology

[0002] Frequency Diverse Array (FDA) introduces small frequency offsets between the transmitting elements of a phased array, thereby generating a three-dimensional transmission pattern in space that is correlated with time, angle, and range. Compared with traditional phased array radar, it adds range-related information, overcoming the problem that phased array radar cannot provide range-related information. FDA-MIMO radar combines FDA with Multiple-Input Multiple-Output (MIMO) technology, transmitting orthogonal waveforms and performing matched filtering at the receiver to obtain the range dimension of freedom, thus achieving the estimation of target range and angle. Based on the advantage of FDA-MIMO radar in simultaneously acquiring range and angle information through spatial processing methods, joint estimation methods for multi-dimensional parameters of FDA-MIMO radar have received widespread attention. Following traditional subspace-based DOA estimation techniques, some scholars have gradually extended subspace-based algorithms to two dimensions and applied them to FDA-MIMO radar, such as the 2D-MUSIC algorithm and the 2D-ESPRIT algorithm; others have proposed algorithms that combine the MUSIC and ESPRIT algorithms to achieve two-dimensional parameter estimation of the target.

[0003] Subspace-based algorithms are very mature and have good parameter estimation accuracy. However, they have certain requirements on the number of snapshots of the received signal and the correlation between signals. A large number of snapshots need to be collected to ensure estimation accuracy, and the estimation performance is severely degraded when the signal source is coherent.

[0004] The emergence of compressed sensing (CS) theory has spurred the rapid development of parameter estimation and sparse reconstruction theories. Combining CS theory with direction of arrival (DOA) estimation in array signal processing effectively overcomes the shortcomings of traditional subspace-based algorithms. Due to its lower required snapshot count and better noise resistance, CS algorithms have become a new approach for joint target range-angle estimation. Based on CS theory, the incremental range and angle of the target across the entire spatial domain can be divided into a grid. By leveraging the target's sparsity in the spatial domain and combining it with a sparse signal reconstruction algorithm, the estimated values ​​of the target range and angle can be obtained.

[0005] However, in existing mesh-based compressed sensing parameter estimation methods, the density of the mesh affects the accuracy of parameter estimation. If the mesh is too sparse, mesh mismatch will occur, while if the mesh is too dense, although the estimation accuracy can be guaranteed, the computational load will increase sharply, affecting the efficiency of parameter estimation. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention provides an FDA-MIMO radar incremental range-angle joint estimation method. The technical problem to be solved by this invention is achieved through the following technical solution:

[0007] This invention provides an FDA-MIMO radar incremental range-angle joint estimation method, including the following steps:

[0008] Signal models for incremental range and angle are established using echo data from FDA-MIMO radar;

[0009] The incremental range information and angle information in the signal model are separated to establish a decoupled model of incremental range and angle for FDA-MIMO radar.

[0010] Based on the decoupling model, the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target is defined. The problem of minimizing the two-dimensional atomic norm is transformed into a first semi-positive definite programming problem, and the first semi-positive definite programming problem is used as the parameter estimation function.

[0011] The incremental distance and angle estimates of the target are calculated based on the parameter estimation function.

[0012] In one embodiment of the present invention, a signal model for incremental range and angle is established using echo data from an FDA-MIMO radar, including:

[0013] Based on the transmit and receive steering vectors of the FDA-MIMO radar, the echo data received by each snapshot array element is arranged into a vector form to obtain the echo data vector:

[0014]

[0015] Where l represents the l-th snapshot. This represents the signal received by the nth receiving element after passing through matched filtering and sampling within its range cell, where N represents the number of transmitting elements, M represents the number of receiving elements, and t... * τ represents the instantaneous moment when data is collected from each distance cell under ideal conditions. * Δτ represents the actual sampling time of the target, and t represents the actual sampling time of the target. * With τ *The difference, Δτ∈[-1 / 2B,1 / 2B], θ0 represents the angle of any stationary target in the far field of space under narrowband conditions, a t (Δτ,θ0) represents the launch steering vector, b r (θ0) represents the receiving steering vector. ξ represents the complex echo amplitude, f0 represents the reference carrier frequency, and τ1 represents the propagation delay of the signal transmitted by the first transmitting element to the target.

[0016] Noise is considered in the echo data vector to obtain the echo signal received by the FDA-MIMO radar receiver for each snapshot. The echo signal is then used as the signal model.

[0017]

[0018]

[0019] Among them, X l This represents the echo signal of the l-th snapshot, n l Let represent Gaussian white noise, δ = 2ΔfΔτ and |δ| ≤ Δf / B, where B represents the bandwidth of the radar baseband waveform, and ⊙ represents the Hadamard product. c is the speed of light. This represents the output of the s-th filter that matches the m-th transmitted waveform, i.e. a t (δ)=[1,exp{-jπδ},...,exp{-jπ(M-1)δ}] T Δf is the frequency offset.

[0020] In one embodiment of the present invention, the decoupling model is:

[0021]

[0022] in, L represents the number of snapshots. F(θ)=[f(θ1),f(θ2),...,f(θ K )], By extracting A column vector formed by M+N-1 non-redundant elements t (δ)=[a t (δ1),a t (δ2),...a t (δ K )],ξ l =[ξ 1l ,ξ 2l ,...ξ Kl ],,ξkl This represents the amplitude of the echo of the k-th target captured in the l-th snapshot. Represents the Khatri-Rao product. This represents the extraction matrix, satisfying P = [P1; P2; ...; P...]. N ], P i The nth row has a 1 at index 1+(i-1)M+(M+1)(η-1), and all other positions have a 0.

[0023] In one embodiment of the present invention, a two-dimensional atomic norm for the incremental range and angle of the FDA-MIMO radar target is defined based on the decoupling model, and the problem of minimizing the two-dimensional atomic norm is transformed into a first semi-positive definite programming problem to obtain a parameter estimation function, including:

[0024] Assuming L snapshots, the two-dimensional atom set for the incremental range and angle of the FDA-MIMO radar target is defined using the decoupling model as follows:

[0025]

[0026] By linearly combining each atom in the two-dimensional atom set, a combination matrix is ​​obtained:

[0027]

[0028] Among them, X s For atomic set A linear combination of K atoms, ρ k =||ξ k,: ||2,ν k =ξ k ,: / ||ξ k,: ||2,

[0029] The combined matrix is ​​used Norm representation yields the two-dimensional atomic norm:

[0030]

[0031] Minimizing the two-dimensional atomic norm and performing convex relaxation yields the first objective function:

[0032]

[0033] Where T(u) represents the Hermitian-two-dimensional block Toplitz matrix:

[0034]

[0035] T i(i = 0, 1, ..., M + N - 2) is:

[0036]

[0037] By incorporating noise into the first objective function, we obtain the first semidefinite programming problem:

[0038]

[0039] Where μ is the regularization coefficient, ||·|| F Denotes the Frogenius norm;

[0040] The first semidefinite programming problem is used as the parameter estimation function.

[0041] In one embodiment of the present invention, after defining the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target based on the decoupling model, and transforming the minimization problem of the two-dimensional atomic norm into a first semi-positive definite programming problem, the method further includes the following steps:

[0042] The main components of the echo data are extracted based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, resulting in a second semi-positive definite programming problem, which is then used as the parameter estimation function.

[0043] In one embodiment of the present invention, the principal components of the echo data are extracted based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, resulting in a second semi-positive definite programming problem, including:

[0044] When the number of snapshots is greater than or equal to the number of targets, perform singular value decomposition on the combined matrix:

[0045]

[0046] in, and All are unitary matrices. The elements on the main diagonal are singular values;

[0047] Based on the decomposition result of the combined matrix, the first objective function is equivalent to the second objective function:

[0048]

[0049] By incorporating noise into the second objective function, we obtain the second semidefinite programming problem:

[0050]

[0051] In one embodiment of the present invention, calculating the incremental distance estimate and angle estimate of the target based on the parameter estimation function includes:

[0052] The parameter estimation function is solved using the CVX toolbox in Matlab to obtain the target matrix with rotation invariant properties;

[0053] By utilizing the rotation-invariant property of the target matrix and combining it with the Vandermonde decomposition theorem, the incremental distance estimate and angle estimate of the target are calculated.

[0054] Another embodiment of the present invention provides an FDA-MIMO radar incremental range-angle joint estimation device, comprising:

[0055] The signal model building module is used to build incremental range and angle signal models using echo data from FDA-MIMO radar.

[0056] The decoupling model establishment module is used to separate the incremental range information and angle information in the signal model and establish a decoupling model of incremental range and angle for FDA-MIMO radar.

[0057] The two-dimensional atomic norm minimization module is used to define the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target based on the decoupling model, and to transform the minimization problem of the two-dimensional atomic norm into a first semi-positive definite programming problem, and to use the first semi-positive definite programming problem as a parameter estimation function.

[0058] The parameter estimation module is used to calculate the incremental distance estimate and angle estimate of the target based on the parameter estimation function.

[0059] In one embodiment of the present invention, it further includes:

[0060] The singular value decomposition atomic norm minimization module is used to extract the main components of the echo data based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, thereby obtaining a second semi-positive definite programming problem, and using the second semi-positive definite programming problem as the parameter estimation function.

[0061] In one embodiment of the present invention, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when the computer program is executed by a processor, it implements the steps of the method described in the above embodiment.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] The method of this invention defines a two-dimensional atomic norm based on a decoupled model that separates incremental distance information and angle information. It transforms the problem of minimizing the two-dimensional atomic norm into a semi-positive definite programming problem, thereby enabling the direct estimation of the incremental distance and angle of the target in the continuous domain. This method does not require gridding of the spatial domain, can solve the grid mismatch problem, and effectively improves the accuracy and efficiency of parameter estimation results. Attached Figure Description

[0064] Figure 1 A flowchart illustrating an FDA-MIMO radar incremental range-angle joint estimation method provided in an embodiment of the present invention;

[0065] Figure 2 A schematic diagram of incremental distance information provided in an embodiment of the present invention;

[0066] Figure 3 A flowchart illustrating another FDA-MIMO radar incremental range-angle joint estimation method provided in an embodiment of the present invention;

[0067] Figure 4 The image shows the result of incremental range-angle estimation of FDA-MIMO radar using the 2D-ANM algorithm, as provided in an embodiment of the present invention.

[0068] Figure 5 The image shows the results of incremental range-angle estimation of FDA-MIMO radar using the SVD-ANM algorithm, as provided in an embodiment of the present invention.

[0069] Figures 6a-6b This is a comparison chart of the changes in RMSE and SNR for different algorithms provided in embodiments of the present invention;

[0070] Figures 7a-7b The RMSE curves of incremental distance estimation and angle estimation with the number of snapshots provided in the embodiments of the present invention are shown.

[0071] Figures 8a-8b The RMSE curves of incremental distance estimation and angle estimation with the number of array elements provided in the embodiments of the present invention are shown.

[0072] Figure 9 The graph shows the variation of the running time of the 2D-ANM and SVD-ANM algorithms provided in the embodiments of the present invention with snapshots. Detailed Implementation

[0073] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0074] Example 1

[0075] Please see Figure 1 , Figure 1 This is a flowchart illustrating an FDA-MIMO radar incremental range-angle joint estimation method provided in an embodiment of the present invention. This method acquires incremental range information at the receiver of the FDA-MIMO radar, specifically considering the range difference caused by the actual time delay and the ideal sampled value within each range gate, thereby further improving the accuracy of target parameter estimation. The approach is as follows: First, an FDA-MIMO radar incremental range-angle signal model is established; then, an FDA-MIMO radar incremental range-angle decoupling model is established to separate the incremental range and angle information in the received signal at the radar receiver; next, an atomic set of the target incremental range and angle is established, a two-dimensional atomic norm is defined, and the problem of minimizing the two-dimensional atomic norm is transformed into a semi-definite programming (SDP) problem.

[0076] The method includes the following steps:

[0077] S1. Establish signal models for incremental range and angle using echo data from FDA-MIMO radar.

[0078] Specifically, it includes:

[0079] S11. Based on the transmit steering vector and receive steering vector of the FDA-MIMO radar, the echo data received by each receiving element in a snapshot is arranged into a vector form to obtain the echo data vector.

[0080] Specifically, firstly, assuming the number of transmitting and receiving elements in the FDA-MIMO radar system is M and N respectively, and assuming the first element is the reference element, then the transmit carrier frequency of the m-th (m=1,...,M) transmitting element is:

[0081] f m =f0+(m-1)Δf (1)

[0082] Where f0 is the reference carrier frequency and Δf is the frequency offset, the value of which is much smaller than the reference carrier frequency and the bandwidth of the transmitted signal.

[0083] The transmitted signal of the m-th transmitting element can be represented as:

[0084]

[0085] Where E is the total power of the transmitted signal. Let T be the baseband waveform of the m-th transmitting element, and T be the pulse duration.

[0086] In theory, The orthogonality condition must be met, that is:

[0087]

[0088] Where τ is the time offset.

[0089] Consider an arbitrary stationary target in the far field of space under narrowband conditions, with an angle of θ0 and a distance of r0. Choosing the first antenna element as the reference element, the distance from the m-th transmitting element to the target can be expressed as:

[0090] r m =r0-(m-1)dsinθ0 (4)

[0091] Where d is the spacing between array elements.

[0092] Therefore, the propagation delay τ of the signal transmitted by the m-th transmitting element to the target is... m It can be represented as:

[0093]

[0094] Where c is the speed of light.

[0095] Therefore, the signal form when the signal emitted by the m-th transmitting element reaches the target is:

[0096]

[0097] The time delay τ between the signal emitted by the m-th transmitting element and its reflection from the target to the n-th receiving element. n,m It can be represented as:

[0098]

[0099] Therefore, the signal received by the nth receiving element from the mth transmitting element can be represented as:

[0100]

[0101] Where ξ is the amplitude of the complex echo.

[0102] Therefore, the echo signal received by the nth array element can be obtained as follows:

[0103]

[0104] Considering the narrowband condition, therefore, we have Where τ1=2r0 / c is the two-way propagation delay between the antenna element and the target. Therefore:

[0105]

[0106] The signal from each receiving channel is then processed by a set of M matched filters. The expression for the matched filter is:

[0107]

[0108] The output of the matched filter is sampled at a sampling rate of:

[0109] f s =B (12)

[0110] Where B represents the bandwidth of the radar baseband waveform.

[0111] Please see Figure 2 , Figure 2 This is a schematic diagram of incremental distance information provided in an embodiment of the present invention. Figure 2 In the middle, t * τ represents the instantaneous moment when data is collected from each distance cell under ideal conditions. * The actual time delay of the target is represented by Δτ, and the incremental distance Δτ represents the difference between the two, i.e.:

[0112] Δτ=t * -τ * (13)

[0113] Where Δτ∈[-1 / 2B,1 / 2B].

[0114] Therefore, based on the above model and the expression for the matched filter in formula (11), the signal received by the nth receiving element after being sampled within its range cell by the matched filter can be expressed as:

[0115]

[0116] In the l-th snapshot, the echo data received by the N receiving elements from the M transmitting elements can be arranged into an MN×1 dimensional vector:

[0117]

[0118] in,[·] T This represents the matrix transpose, where l represents the l-th snapshot. This represents the signal received by the nth receiving element after passing through matched filtering and sampling within its range cell, where N represents the number of transmitting elements, M represents the number of receiving elements, and t... * τ represents the instantaneous moment when data is collected from each distance cell under ideal conditions. * Δτ represents the actual sampling time of the target, and t represents the actual sampling time of the target. * With τ * The difference, Δτ∈[-1 / 2B,1 / 2B], where θ0 represents the angle of any stationary target in the far field of space under narrowband conditions. Indicates the launch steering vector. Indicates the receiving guide vector. f0 represents the reference carrier frequency, and τ1 represents the propagation delay of the signal transmitted by the first transmitting element to the target.

[0119] The launch guidance vector is represented as:

[0120] a t (Δτ,θ0)=a t (θ0)⊙a t (Δτ) (16)

[0121] Where ⊙ represents the Hadamard product, The expression for c(θ0) is:

[0122]

[0123] This represents the output of the s-th filter that matches the m-th transmitted waveform.

[0124] a t (Δτ)=[1,exp{-j2πΔfΔτ},...,exp{-j2π(M-1)ΔfΔτ}] T (18)

[0125] The receiving guidance vector is represented as:

[0126]

[0127] Next, let δ = 2ΔfΔτ (|δ|≤Δf / B) in formula (18), then u(Δτ,θ0) can be further expressed as:

[0128]

[0129] Among them, a t (δ) is represented as:

[0130] a t (δ)=[1,exp{-jπδ},...,exp{-jπ(M-1)δ}] T (twenty one)

[0131] As can be seen from formula (21), the incremental distance information δ and the angle information θ0 of the target are coupled together in the guide vector a(δ,θ0), which may lead to ambiguity in the estimation results.

[0132] S12. Noise is considered in the echo data vector to obtain the echo signal received by each snapshot based on the FDA-MIMO radar receiver, and the echo signal is used as the signal model.

[0133] Specifically, considering noise, the signal expression for the l-th snapshot received by the receiver is:

[0134]

[0135] Among them, X l This represents the echo signal of the l-th snapshot, n l This represents Gaussian white noise.

[0136] S2. Separate the incremental range information and angle information in the signal model to establish a decoupled model of incremental range and angle for FDA-MIMO radar.

[0137] Specifically, firstly, regarding X in formula (22) l Applying the vectorization operator, we obtain:

[0138]

[0139] Where, n l =vec(N l ), It represents the Kronecker product.

[0140] Then, a series of mathematical transformations are performed on formula (23), as shown in formula (24):

[0141]

[0142] Among them, 1 N Let diag(D) represent an N×1 dimensional column vector where all elements are 1. Let diag(D) represent extracting the main diagonal of D as a column vector.

[0143] Define a column vector It is through extraction It is formed by M+N-1 non-redundant elements, therefore, formula (24) can be rewritten as:

[0144]

[0145] The operator diag(D,k) returns the kth diagonal of D.

[0146] Next, construct an extraction matrix. Satisfying P = [P1; P2; ...; P N ],in P i The nth row has a 1 at index 1+(i-1)M+(M+1)(η-1), and all other positions have 0. Therefore, equation (25) can be rewritten as:

[0147]

[0148] Among them, F(θ)=[f(θ1),f(θ2),...,f(θ K )],A t (δ)=[a t (δ1),a t (δ2),...a t (δ K )],ξ l =[ξ 1l ,ξ 2l ,...ξ Kl ], ξ kl This represents the amplitude of the echo of the k-th target captured in the l-th snapshot. This represents the Khatri-Rao product.

[0149] Therefore, the received signals of L snapshots are represented as:

[0150]

[0151] in,

[0152] Formula (27) is the decoupled signal model of the range-angle of the FDA-MIMO radar received signal.

[0153] S3. Based on the decoupling model, define the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target, and transform the minimization problem of the two-dimensional atomic norm into a first semi-positive definite programming problem, and use the first semi-positive definite programming problem as the parameter estimation function.

[0154] This step proposes an incremental distance-angle joint estimation algorithm based on 2-Dimensional-Atomic Norm Minimization (2D-ANM). Specifically, it includes:

[0155] First, assuming L snapshots, the two-dimensional atom set for the incremental range and angle of the FDA-MIMO radar target is defined using the decoupling model as follows:

[0156]

[0157] Then, a new matrix is ​​defined according to formula (28). Specifically, each atom in the two-dimensional atom set of formula (28) is linearly combined to obtain the combination matrix:

[0158]

[0159] Among them, X s For atomic set A linear combination of K atoms, ρk =||ξ k,: ||2,ν k =ξ k ,: / ||ξ k,: ||2,

[0160] According to CS theory, The norm can represent the sparsity of the received signal. Equation (29) for the combination matrix... The norm is:

[0161]

[0162] Where κ represents the κ-th target, ν k To represent ν in vector form, inf(·) denotes the infimum operator.

[0163] Since the problem in formula (30) is an NP-hard problem and there is no efficient solution, it is usually used in practice. Norm substitution, Norm representation of pairs Convex relaxation of the norm. That is, combining the matrix of equation (29) using... Norm representation yields the two-dimensional atomic norm:

[0164]

[0165] Then, by minimizing the two-dimensional atomic norm and performing convex relaxation, equation (31) is transformed into the following SDP problem, yielding the first objective function:

[0166]

[0167] Where V is the value of ν k Represented in matrix form, T(u) denotes the Hermitian-toeplitz matrix:

[0168]

[0169] T i (i = 0, 1, ..., M + N - 2) is:

[0170]

[0171] By considering noise in the first objective function, the first objective function of formula (32) is further modified to obtain the first semidefinite programming problem:

[0172]

[0173] Where μ is the regularization coefficient, ||·|| F This represents the Frogenius norm.

[0174] The first semidefinite programming problem of formula (35) is used as the parameter estimation function.

[0175] S4. Calculate the incremental distance estimate and angle estimate of the target based on the parameter estimation function.

[0176] Specifically, the parameter estimation function (i.e., the first positive definite programming problem) is first solved using the CVX toolbox in Matlab to obtain the target matrix T(u) with rotation invariance. Then, using the rotation invariance of the target matrix T(u) and the Vandermonde decomposition theorem, the incremental distance and angle estimates of the target are calculated.

[0177] The specific calculations in step S4 are existing technologies and will not be described in detail in this embodiment.

[0178] The method described in this embodiment is a meshless compressed sensing algorithm. This method defines a two-dimensional atomic norm based on a decoupled model that separates incremental distance and angle information. It transforms the minimization problem of the two-dimensional atomic norm into a semi-positive definite programming problem, thereby directly estimating the incremental distance and angle of the target in the continuous domain. This method does not require meshing of the spatial domain, solving the mesh mismatch problem and effectively improving the accuracy of the parameter estimation results. Furthermore, this method can achieve high-precision estimation even with limited snapshots.

[0179] Example 2

[0180] Based on Example 1, please refer to Figure 3 , Figure 3 A flowchart illustrating another FDA-MIMO radar incremental range-angle joint estimation method provided in this embodiment of the invention.

[0181] The method includes the following steps:

[0182] S1. Establish signal models for incremental range and angle using echo data from FDA-MIMO radar.

[0183] S2. Separate the incremental range information and angle information in the signal model to establish a decoupled model of incremental range and angle for FDA-MIMO radar.

[0184] S3. Based on the decoupling model, define the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target, and transform the minimization problem of the two-dimensional atomic norm into a first semidefinite programming problem.

[0185] For the specific implementation steps of steps S1, S2, and S3, please refer to Example 1. This example will not repeat them.

[0186] S4. Extract the main components of the echo data based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, and obtain the second semi-positive definite programming problem. Use the second semi-positive definite programming problem as the parameter estimation function.

[0187] In the first semidefinite programming problem obtained in step S3, the dimension of the semidefinite matrix increases with the number of snapshots, leading to a significant increase in algorithm complexity and a decrease in computational efficiency due to the increase in the number of received signal snapshots. Therefore, step S4 further extracts the main components of the received signal based on singular value decomposition, thereby reducing the dimension of the first semidefinite matrix. This step proposes an incremental distance-angle joint estimation algorithm based on Singular Value Decomposition-Atomic Norm Minimization (SVD-ANM), specifically including:

[0188] Ignoring noise, when the number of snapshots is greater than or equal to the number of targets, i.e., L≥K, the combination matrix X of formula (29) is... s Singular value decomposition yields:

[0189]

[0190] in, and All are unitary matrices. The elements on the main diagonal are singular values. Therefore, we can obtain:

[0191]

[0192] in,

[0193] Based on the decomposition result of the combined matrix, the first objective function is equivalent to the second objective function. Specifically, let... Therefore, the first objective function of formula (32) can be equivalent to the second objective function, expressed as:

[0194]

[0195] in, and With V and X in the first objective function s They have the same meaning, only expressed in different forms.

[0196] Then, considering noise in the second objective function, the second objective function of formula (38) can be further expressed as:

[0197]

[0198] in, The construction method and The construction method is similar.

[0199] Formula (38) is the second semidefinite programming problem, which is used as the parameter estimation function. The dimension of the constraint matrix of the objective function of Formula (38) is no longer related to the number of snapshots, which means that when the number of snapshots of the received signal increases, its computational efficiency will not be affected. Therefore, in scenarios with a large number of snapshots, this algorithm can effectively reduce computational complexity.

[0200] S5. Calculate the incremental distance estimate and angle estimate of the target based on the parameter estimation function.

[0201] Specifically, the parameter estimation function (i.e., the second positive definite programming problem) is first solved using the CVX toolbox in Matlab to obtain the target matrix T(u) with rotation invariance. Then, using the rotation invariance of the target matrix T(u) and the Vandermonde decomposition theorem, the incremental distance and angle estimates of the target are calculated.

[0202] The method in this embodiment can effectively reduce computational complexity and improve the efficiency of parameter estimation. At the same time, this method can achieve high-precision estimation even with fewer snapshots.

[0203] Example 3

[0204] Based on Examples 1 and 2, this example further illustrates the incremental distance-angle joint estimation algorithm based on 2D-ANM in Example 1 and the incremental distance-angle joint estimation algorithm based on SVD-ANM in Example 2 through simulation.

[0205] As shown in Table 1, Table 1 is a simulation parameter table of the gridless compressed sensing FDA-MIMO radar incremental range-angle joint estimation method provided in the embodiments of the present invention.

[0206] Table 1

[0207] parameter Parameter value parameter Parameter value Number of launch array elements 10 Array element spacing 0.015m Number of receiving array elements 10 carrier frequency 10GHz Frequency offset 500kHz signal bandwidth 0.25MHz Incremental distance scan range 0～1 / (2B) Angle scanning range -90°～90°

[0208] Simulation 1: Verifying the effectiveness of the 2D-ANM algorithm and the SVD-ANM algorithm.

[0209] Assume there are three point targets in the far field of space with incremental range-angle values ​​of (0.5 μs, -20°), (0.5 μs, 40°), and (1 μs, 40°). The number of snapshots is set to 10, the signal-to-noise ratio to be 10 dB, and the number of Monte Carlo trials is 200. Please refer to [link / reference]. Figure 4 and Figure 5 , Figure 4 This is a result image of incremental range-angle estimation of FDA-MIMO radar using the 2D-ANM algorithm, provided in an embodiment of the present invention. Figure 5 The image shows the results of incremental range-angle estimation of FDA-MIMO radar using the SVD-ANM algorithm, as provided in an embodiment of the present invention. Figure 4 and Figure 5 The results show that, regardless of whether the targets are at the same distance but different angles or at different distances but the same angle, both algorithms can accurately estimate the distance and angle of three targets with a finite number of snapshots (L << MN).

[0210] Simulation 2: RMSE variation of parameter estimation by 2D-ANM and SVD-ANM algorithms with SNR, and comparison with traditional algorithms.

[0211] In this experiment, the number of snapshots was set to 10, the signal-to-noise ratio ranged from [-10, 15] dB, the number of far-field point targets was considered to be 1, and the corresponding distance increment-angle parameter was (1 μs, 20°). The number of Monte Carlo trials was 200. Other simulation parameters are shown in Table 1. Then, the RMSE curves of parameter estimation as a function of SNR for the 2D-ANM algorithm, SVD-ANM algorithm, traditional two-dimensional subspace algorithms (2D-MUSIC, 2D-ESPRIT) and grid-based compressed sensing algorithms (2D-OMP, 2D-IAA) were compared and analyzed.

[0212] Please see Figures 6a-6b , Figures 6a-6b This is a comparison chart showing the variation of RMSE with SNR for different algorithms provided in embodiments of the present invention. Figure 6a (a) Plot showing the variation of incremental distance RMSE with SNR. Figure 6b (b) The graph shows the change of RMSE for angle with SNR. As can be seen from the graph, the RMSE of the parameter estimation for all these algorithms gradually decreases with increasing SNR. However, the RMSE of the 2D-ANM and SVD-ANM algorithms is closer to the CRB, exhibiting the best accuracy in joint estimation of target incremental distance and angle. For the 2D-OMP and 2D-IAA algorithms, although the target falls on the grid, their parameter estimation performance is still weaker than that of the 2D-ANM and SVD-ANM algorithms based on meshless compressed sensing. For the subspace-based 2D-MUSIC and 2D-ESPRIT algorithms, they typically require a large number of snapshots to achieve high estimation accuracy, while the estimation effect is poor with a small number of snapshots.

[0213] Simulation 3: RMSE of parameter estimation using 2D-ANM and SVD-ANM algorithms as a function of snapshot number, and comparison with traditional algorithms.

[0214] This simulation compares the changes in RMSE of the estimated values ​​of each algorithm in Simulation 2 with the number of snapshots. SNR is set to 5dB, and the number of snapshots ranges from [5,30].

[0215] Experimental results are as follows Figures 7a-7b As shown, Figures 7a-7b The curves showing the RMSE variation with the number of snapshots for incremental distance estimation and angle estimation provided in the embodiments of the present invention are as follows. Figure 7a This is a graph showing how incremental distance RMSE changes with the number of snapshots. Figure 7b The graph shows the variation of the angle RSME with the number of snapshots. As can be seen from the graph, the RMSE of parameter estimation for both meshless compressed sensing-based algorithms (2D-ANM, SVD-ANM) and subspace-based algorithms (2D-MUSIC, 2D-ESPRIT) gradually decreases with increasing snapshot count. However, the RMSE of parameter estimation for mesh-based compressed sensing algorithms (2D-OMP, 2D-IAA) is unaffected by the number of snapshots; its RMSE remains essentially unchanged with increasing snapshot count. Compared to other algorithms, the 2D-ANM and SVD-ANM algorithms still achieve the best estimation accuracy with the lowest RMSE, indicating that these two algorithms can still guarantee their estimation accuracy under limited snapshot conditions.

[0216] Simulation 4: RMSE of parameter estimation using 2D-ANM and SVD-ANM algorithms as a function of the number of array elements, and comparison with traditional algorithms.

[0217] This simulation compares the RMSE of the estimates from each algorithm in Simulation 1 as a function of the number of array elements. The SNR was set to 5 dB and the number of snapshots was 10.

[0218] Experimental results are as follows Figures 8a-8b As shown, Figures 8a-8b The curves showing the variation of RMSE with the number of array elements for incremental distance estimation and angle estimation using several algorithms provided in this embodiment of the invention are as follows. Figure 8a This is a graph showing the variation of incremental distance RMSE with the number of array elements. Figure 8b The graph shows the change in RMSE of the angle with the number of array elements. As can be seen from the graph, the RMSE of these algorithms gradually decreases with the increase of the number of array elements, but the 2D-ANM algorithm and the SVD-ANM algorithm have better estimation performance than the other algorithms.

[0219] Simulation 5: Running time of 2D-ANM and SVD-ANM algorithms as a function of snapshot number.

[0220] This experiment simulates and analyzes the running time of the 2D-ANM and SVD-ANM algorithms as a function of the number of snapshots, verifying whether the SVD-ANM algorithm effectively reduces computational complexity. Similarly, considering that the number of far-field point targets is 1, its corresponding distance increment-angle parameter is (1µs, 20µs). ° The SNR was set to 5dB, the number of snapshots ranged from [10, 50], and the number of Monte Carlo trials was 200. Other simulation parameters are shown in Table 1.

[0221] Experimental results are as follows Figure 9 As shown, Figure 9 The graph shows the runtime of the 2D-ANM and SVD-ANM algorithms as a function of snapshots, as provided in this embodiment of the invention. As can be seen from the graph, the runtime of the 2D-ANM algorithm increases continuously with the number of snapshots, while the runtime of the SVD-ANM algorithm remains essentially unchanged, unaffected by the number of snapshots. This demonstrates that the SVD-ANM algorithm effectively reduces computational complexity and improves computational efficiency; in scenarios with a large number of snapshots, its computational efficiency is significantly better than that of the 2D-ANM algorithm.

[0222] Example 4

[0223] Based on Embodiments 1 and 2, this embodiment provides an FDA-MIMO radar incremental range-angle joint estimation device, comprising:

[0224] The signal model building module is used to build incremental range and angle signal models using echo data from FDA-MIMO radar.

[0225] The decoupling model establishment module is used to separate the incremental range information and angle information in the signal model and establish a decoupling model of incremental range and angle for FDA-MIMO radar.

[0226] The two-dimensional atomic norm minimization module is used to define the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target based on the decoupling model, and to transform the minimization problem of the two-dimensional atomic norm into a first semi-positive definite programming problem, and to use the first semi-positive definite programming problem as a parameter estimation function.

[0227] The parameter estimation module is used to calculate the incremental distance estimate and angle estimate of the target based on the parameter estimation function.

[0228] In one specific embodiment, the FDA-MIMO radar incremental range-angle joint estimation device further includes: a singular value decomposition atomic norm minimization module, used to extract the main components of the echo data based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem to obtain a second semi-positive definite programming problem, and to use the second semi-positive definite programming problem as the parameter estimation function.

[0229] The FDA-MIMO radar incremental range-angle joint estimation device provided in this embodiment can execute the above method embodiment. Its implementation principle and technical effect are similar, and will not be described again here.

[0230] Example 5

[0231] This embodiment provides a computer program stored thereon, which, when executed by a processor, implements the steps shown in Embodiment 1 and / or Embodiment 2.

[0232] The computer-readable storage medium provided in this embodiment can execute the above method embodiment. Its implementation principle and technical effect are similar, and will not be described again here.

[0233] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0234] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0235] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0236] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0237] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0238] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

[0239] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A joint range-angle estimation method for FDA-MIMO radar, characterized in that, Including the following steps: Based on the transmit and receive steering vectors of the FDA-MIMO radar, the echo data received by each snapshot array element is arranged into a vector form to obtain the echo data vector: ； ； in, Indicates the first A quick snapshot, Indicates the first n The received signal of each receiving array element is obtained after matched filtering and sampling within its range cell. Indicates the number of receiving array elements. Indicates the number of transmitting array elements. m Indicates the first m Each launch array element ， This represents the instantaneous moment when data is collected from each distance cell under ideal conditions. Indicates the actual sampling time of the target. express and The difference, , This represents the angle of any stationary target in the far field of space under narrowband conditions. Indicates the launch steering vector. Indicates the receiving guide vector. , Indicates the amplitude of the complex echo. Indicates the reference carrier frequency. This represents the propagation delay of the signal emitted by the first transmitting element to reach the target. , d For the spacing between array elements, c The speed of light; Noise is considered in the echo data vector to obtain the echo signal received by the FDA-MIMO radar receiver for each snapshot. The echo signal is then used as a signal model. ； ； in, Indicates the first A quick snapshot of the echo signal, This represents Gaussian white noise. and , B Indicates the bandwidth of the radar baseband waveform. Represents the Hadamard product. , , c At the speed of light, Indicates the relationship with the first m The first transmission waveform matches the s The output of each filter, i.e. , , This is the frequency offset. ; The incremental range information and angle information in the signal model are separated to establish a decoupled model of incremental range and angle for FDA-MIMO radar. Based on the decoupling model, the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target is defined. The problem of minimizing the two-dimensional atomic norm is transformed into a first semi-positive definite programming problem, and the first semi-positive definite programming problem is used as the parameter estimation function. The incremental distance and angle estimates of the target are calculated based on the parameter estimation function.

2. The FDA-MIMO radar incremental range-angle joint estimation method according to claim 1, characterized in that, The decoupling model is as follows: ； in, , , , Indicates the number of snapshots. , , By extracting of M + N A column vector consisting of -1 non-redundant elements. , , Indicates the first l The first quick shot k The amplitude of the echo of each target, Represents the Khatri-Rao product. Let P be the extraction matrix, satisfying P = [P1; P2; ...; P N ], , The Rows at index The position is 1, and the rest are 0.

3. The FDA-MIMO radar incremental range-angle joint estimation method according to claim 2, characterized in that, Based on the decoupling model, a two-dimensional atomic norm is defined for the incremental range and angle of the FDA-MIMO radar target. The problem of minimizing the two-dimensional atomic norm is transformed into a first semi-positive definite programming problem, resulting in a parameter estimation function, including: Assuming in L In a single snapshot, using the aforementioned decoupling model, the two-dimensional atom set for the incremental range and angle of the FDA-MIMO radar target is defined as follows: ； By linearly combining each atom in the two-dimensional atom set, a combination matrix is ​​obtained: ； in, For atomic set middle K A linear combination of atoms, , , ; The combined matrix is ​​used Norm representation yields the two-dimensional atomic norm: ； in, Indicate the infimum operator; Minimizing the two-dimensional atomic norm and performing convex relaxation yields the first objective function: ； in, To be Represented as a matrix, Representing the Hermitian-2D block Toplitz matrix: ； for: ； By incorporating noise into the first objective function, we obtain the first semidefinite programming problem: ； in, The regularization coefficient is . Denotes the Frogenius norm; The first semidefinite programming problem is used as the parameter estimation function.

4. The FDA-MIMO radar incremental range-angle joint estimation method according to claim 3, characterized in that, Based on the decoupling model, the two-dimensional atomic norms of the incremental range and angle of the FDA-MIMO radar target are defined. After the problem of minimizing the two-dimensional atomic norms is transformed into a first semi-positive definite programming problem, the following steps are also included: The main components of the echo data are extracted based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, resulting in a second semi-positive definite programming problem, which is then used as the parameter estimation function.

5. The FDA-MIMO radar incremental range-angle joint estimation method according to claim 4, characterized in that, Based on singular value decomposition, the main components of the echo data are extracted to reduce the dimensionality of the first semi-positive definite programming problem, resulting in a second semi-positive definite programming problem, including: When the number of snapshots is greater than or equal to the number of targets, perform singular value decomposition on the combined matrix: ； in, and All are unitary matrices. The elements on the main diagonal are singular values; Based on the decomposition result of the combined matrix, the first objective function is equivalent to the second objective function: ； in, , , To count the number of snapshots, For the target number, To be Represented as a matrix; By incorporating noise into the second objective function, we obtain the second semidefinite programming problem: 。 6. The FDA-MIMO radar incremental range-angle joint estimation method according to claim 1 or 4, characterized in that, The incremental distance and angle estimates of the target are calculated based on the parameter estimation function, including: The parameter estimation function is solved using the CVX toolbox in Matlab to obtain the target matrix with rotation invariant properties; By utilizing the rotation-invariant property of the target matrix and combining it with the Vandermonde decomposition theorem, the incremental distance estimate and angle estimate of the target are calculated.

7. An FDA-MIMO radar incremental range-angle joint estimation device, characterized in that, include: The signal model building module is used to build incremental range and angle signal models using echo data from the FDA-MIMO radar. This includes: arranging the echo data received by each receiving element in a vector form based on the transmit and receive steering vectors of the FDA-MIMO radar to obtain the echo data vector. ； ； in, Indicates the first A quick snapshot, Indicates the first n The received signal of each receiving array element is obtained after matched filtering and sampling within its range cell. Indicates the number of receiving array elements. Indicates the number of transmitting array elements. m Indicates the first m Each launch array element ， This represents the instantaneous moment when data is collected from each distance cell under ideal conditions. Indicates the actual sampling time of the target. express and The difference, , This represents the angle of any stationary target in the far field of space under narrowband conditions. Indicates the launch steering vector. Indicates the receiving guide vector. , Indicates the amplitude of the complex echo. Indicates the reference carrier frequency. This represents the propagation delay of the signal emitted by the first transmitting element to reach the target. , d For the spacing between array elements, c The speed of light; Noise is considered in the echo data vector to obtain the echo signal received by the FDA-MIMO radar receiver for each snapshot. The echo signal is then used as the signal model. ； ； in, Indicates the first A quick snapshot of the echo signal, This represents Gaussian white noise. and , B Indicates the bandwidth of the radar baseband waveform. Represents the Hadamard product. , , c At the speed of light, Indicates the relationship with the first m The first transmission waveform matches the s The output of each filter, i.e. , , This is the frequency offset. ; The decoupling model establishment module is used to separate the incremental range information and angle information in the signal model and establish a decoupling model of incremental range and angle for FDA-MIMO radar. The two-dimensional atomic norm minimization module is used to define the two-dimensional atomic norm of the incremental range and angle of the FDA-MIMO radar target based on the decoupling model, and to transform the minimization problem of the two-dimensional atomic norm into a first semi-positive definite programming problem, and to use the first semi-positive definite programming problem as a parameter estimation function. The parameter estimation module is used to calculate the incremental distance estimate and angle estimate of the target based on the parameter estimation function.

8. The FDA-MIMO radar incremental range-angle joint estimation device according to claim 7, characterized in that, Also includes: The singular value decomposition atomic norm minimization module is used to extract the main components of the echo data based on singular value decomposition to reduce the dimensionality of the first semi-positive definite programming problem, thereby obtaining a second semi-positive definite programming problem, and using the second semi-positive definite programming problem as the parameter estimation function.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method described in any one of claims 1-6.

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