A sparse reconstruction elevation angle estimation method for off-grid targets

Abstract

The application discloses a sparse reconstruction elevation angle estimation method for an off-grid target, and has the characteristics that the echo signal of the target is subjected to L times of digital sampling shots based on a target distance unit, L times of digital sampling shot data of M antenna array elements are obtained, a sampling matrix is processed through a singular value decomposition technology, and a reduced dimension echo data vector is obtained; a search space dictionary is constructed, and the whole search space dictionary is divided into J parts; an orthogonal matching pursuit algorithm is used to preliminarily estimate the elevation angle of the target, an initial estimated elevation angle of the target and a corresponding K target sparse coefficient vector are obtained; based on the initial estimated elevation angle of the target and the sparse coefficient vector, the estimation of the grid disturbance and the target sparse vector is updated through an alternating iteration method, the grid point is updated to the real elevation angle position of the target through the grid disturbance, and then the elevation angle estimation value of the target is obtained. The application improves the angle estimation performance of the radar on the low-altitude target.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a sparse reconstruction elevation angle estimation method for off-network targets, applicable to meter-wave radar for estimating the elevation angle of low-altitude targets. Background Technology

[0002] With the development of aircraft flight technology in recent years, the demand for higher accuracy in radar target detection methods has become increasingly urgent. However, due to the wide beam of meter-wave radar, when detecting targets moving at low altitudes, it is affected by multipath echoes reflected from the ground. Strongly coherent direct wave signals and multipath reflected signals are simultaneously received by the radar receiver array from the same beam, severely impacting the elevation angle estimation performance of meter-wave radar. Therefore, improving the low-elevation-angle target measurement performance of meter-wave radar is one of the key issues for achieving superior performance in meter-wave radar.

[0003] In recent years, super-resolution algorithms based on array signals have been applied to elevation angle estimation for meter-wave radar. A typical example is the sparse reconstruction algorithm, whose greatest advantage lies in not requiring a known number of signal sources, being unaffected by coherence, and achieving good elevation angle estimation accuracy with a relatively small number of snapshots. This solves the problem of excessively high snapshot requirements for feature subspace algorithms, providing an effective solution for meeting real-time requirements in low-elevation angle measurement scenarios. However, a drawback is that the sparse reconstruction algorithm estimates elevation angles by dividing the airspace into several grids to form a dictionary. For targets outside the grid that do not fall on any grid points, only the nearest grid point can be used for approximation, which leads to significant limitations in the accuracy of elevation angle estimation for these targets. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a sparse reconstruction elevation angle estimation method for off-grid targets. The technical problem to be solved by this invention is achieved through the following technical solution:

[0005] A sparse reconstruction elevation angle estimation method for off-grid targets, the sparse reconstruction elevation angle estimation method comprising:

[0006] Step 1: The meter-wave array radar transmits an M-dimensional signal to the target within its detection range and then receives the echo signal from the target.

[0007] Step 2: Perform L digital sampling snapshots on the echo signal of the target based on the target range element to obtain L digital sampling snapshot data of M antenna array elements;

[0008] Step 3: Obtain the sampling matrix based on the l-th digital sampling snapshot data of the echo of the m-th antenna array element, and process the sampling matrix using singular value decomposition to obtain the dimension-reduced echo data vector, where 0 < m ≤ M;

[0009] Step 4: Based on the angle search range and multipath signal echo model of the meter-wave array radar, construct the search airspace dictionary and divide the entire search airspace dictionary into J parts, where J>M;

[0010] Step 5: Based on the dimension-reduced echo data vector and the search spatial domain dictionary, the orthogonal matching pursuit algorithm is used to make a preliminary estimate of the target's elevation angle, and the initial estimated elevation angle of the target and the sparse coefficient vector of the corresponding K targets are obtained.

[0011] Step 6: Based on the initial estimated elevation angle and sparse coefficient vector of the target, the estimates of the grid perturbation and the target sparse vector are updated by alternating iteration. The grid points are updated to the true elevation angle position of the target through grid perturbation, thereby obtaining the estimated elevation angle of the target.

[0012] In one embodiment of the present invention, the meter-wave array radar comprises M isotropic array elements arranged with half-wavelength spacing and placed perpendicular to the ground plane.

[0013] In one embodiment of the present invention, step 2 includes:

[0014] Step 2.1: By performing pulse compression processing and moving target detection on the echo signal of the target, the target range cell where the target is located is determined;

[0015] Step 2.2: Perform L digital sampling snapshots on the echo signal of the target at the target range unit to obtain L digital sampling snapshot data of the M antenna array elements.

[0016] In one embodiment of the present invention, step 3 includes:

[0017] Step 3.1: Arrange the L digital sampling snapshot data of the echo of the m-th antenna element in order to obtain the sampling vector of the echo of the target detected by the m-th antenna element;

[0018] Step 3.2: Obtain the sampling matrix composed of the sampling vectors of the M antenna array elements based on the sampling vectors of the echoes detected by the M antenna array elements.

[0019] Step 3.3: Perform singular value decomposition on the sampling matrix using singular value decomposition (SVD) technology, decomposing it into an M×M dimensional left singular matrix U, an M×L dimensional matrix Λ, and an L×L dimensional right singular matrix V. H In this matrix Λ, the diagonal elements are singular values ​​and the remaining elements are 0;

[0020] Step 3.4: Based on the sampling matrix and the right singular matrix V H and M×1 dimensional column vectors The reduced-dimensional echo data vector is obtained. It is an L-1 dimensional zero column vector.

[0021] In one embodiment of the present invention, the meter-wave array radar angle search range is [θ start ,θ end ], θ start θ represents the minimum angle search value of the meter-wave array radar. end θ represents the maximum angle search value of the meter-wave array radar, where θ end -θ start ≤θ 3dB θ 3dB This represents the beam half-power width of the signal transmitted by the meter-wave array radar to a target within its detection range.

[0022] In one embodiment of the present invention, step 4 includes:

[0023] Step 4.1: Obtain the direct wave signal data x received by the m-th antenna element. dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t);

[0024] The direct wave signal data x dm (t) is:

[0025]

[0026] Where s(t) is the transmitted signal of the antenna array element, and n m (t) represents the additive white noise of the m-th antenna element channel, θ d The pitch angle of the target to be estimated;

[0027] The multipath wave signal data x mm (t) is:

[0028]

[0029] Where, θ s Let ρ be the multipath elevation angle of the target, ρ be the reflection coefficient, α = 2πΔR / λ be the phase difference between the direct wave and the multipath wave due to time delay, and ΔR be the path difference between the direct wave and the multipath wave.

[0030] Step 4.2: The direct wave signal data x received by the m-th antenna element... dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t) are superimposed to obtain the composite data x received by the m-th antenna element. m (t), and combine the composite data x m (t) is denoted as the echo model of a multipath signal;

[0031] Step 4.3: Based on the composite data x received by the M antenna elements m (t) Obtain the composite data x of M antenna elements m The sampling matrix X(t) is composed of (t);

[0032] Step 4.4: Obtain the composite steering vector Φ based on the sampling matrix X(t). a (θ j The composite guiding vector Φ a (θ j )for:

[0033]

[0034] Where, Φ a To search the spatial domain dictionary, θ j To search for the pitch angle corresponding to the j-th atom in the spatial domain dictionary, a(θ) j ) represents the pitch angle θ j The steering vector Φ under the manifold of this radar array a (θ j ) represents the target in a(θ) j The steering vector represents the composite steering vector of the received signal when the direction is represented, and hr is the height difference from the center of the array to the reflective surface;

[0035] Step 4.5: Based on the angle search range [θ] start ,θ end ], with a fixed search interval The entire spatial domain is discretized into J grids, and the atomic vector of each grid is the corresponding Φ. a (θ j If ), then search the spatial domain dictionary Φ a Represented as an M×J dimensional matrix:

[0036]

[0037] Where, Φ a To search the spatial domain dictionary, a(θ) start ) represents the steering vector for finding the minimum angle of the meter-wave array radar under the radar array manifold, a(θ) end ) is the steering vector for the maximum angle search value of the meter-wave array radar under the radar array manifold.

[0038] In one embodiment of the present invention, step 5 includes:

[0039] Step 5.1: Select the residual e with respect to the current iteration number k. k The dictionary atom with the largest inner product is added to the current support index set to obtain the updated support index set. The dictionary atom is:

[0040]

[0041] Where, λ k Let be the dictionary atom selected for the k-th iteration, <·,·> be the inner product of two vectors, and |·| be the absolute value;

[0042] Step 5.2: Combine the updated support index set into a matrix. Then the orthogonal projection operator P of this atomic space is:

[0043]

[0044] in,[·] T For the transpose operation of a matrix, [·] -1 This is the operation for finding the inversion of a matrix.

[0045] By from residual e k Subtract its in The updated residual e is obtained by the orthogonal projection onto the spanned space. k+1 e k+1 =e k -Pe k ;

[0046] The sparsity coefficient corresponding to the selected dictionary atom is γ. k =Pe k ;

[0047] Step 5.3: Let k = k + 1. At this point, a complete iteration is completed. Return to step 5.1 until the iteration exit requirement k = K is met.

[0048] Step 5.4: Obtain the elevation angle estimates corresponding to K targets based on the dictionary atoms in the support index set after iteration, and obtain the sparse coefficient vector of K targets for the orthogonal matching tracking algorithm based on the sparse coefficients.

[0049] In one embodiment of the present invention, step 6 includes:

[0050] Step 6.1: Introduce the mesh perturbation δθ. When the sparsity is K, the mesh perturbation is:

[0051] δθ=[δθ1, δθ2, δθ3,..., δθ K ]

[0052] Where, δθ k The k-th target is the nearest point in the original dictionary grid, θ. k Unknown disturbances;

[0053] Step 6.2: Obtain the estimation model based on the grid perturbation δθ and the target sparse vector γ;

[0054] Step 6.3: Let t = 1, where t is the current iteration number, and T max To determine the maximum number of iterations for the algorithm, the initial value of the sparse vector of the K targets is the sparse coefficient vector γ obtained in step 5. (1) The initial elevation angle estimates for the K targets are the initial estimated elevation angles θ obtained in step 5. (1) ;

[0055] Step 6.4: Keep the sparse vectors of the K targets unchanged, and optimize the mesh perturbation based on the estimation model;

[0056] Step 6.5: Based on the dimension-reduced echo data vector and the sparse vector γ of the K targets in the t-th iteration... (t) The data residual for the t-th iteration is obtained by combining the corresponding dictionary atoms.

[0057] Step 6.6: Take the partial derivative θ with respect to the variables of each dictionary atom of the K targets in the t-th iteration. k The partial derivatives are obtained, and the partial derivative dictionary matrix A is obtained based on the partial derivatives and the sparse vector of the target. (t) ;

[0058] Step 6.7: Based on the data residuals And partial derivative dictionary matrix A (t) Obtain the new objective function This yields the mesh perturbation amount for the t-th iteration;

[0059] Step 6.8: Obtain the updated dictionary grid point positions based on the grid perturbation amount in the t-th iteration;

[0060] Step 6.9: Keep the dictionary grid positions of the K targets unchanged, optimize the sparse vector of the K targets using the optimization objective function, and obtain the update matrix B based on the updated dictionary grid positions. (t+1) ;

[0061] Step 6.10: Based on the update matrix B (t+1) Based on the closed-form solution of the linear least squares solution, the updated sparse vector of the K objectives is obtained;

[0062] Step 6.11: Let t = t + 1, and determine whether t = T. max If yes, stop iterating; the dictionary grid positions at this point are the elevation angle estimates for the K targets. If no, return to step 6.4 until t = T. max .

[0063] The beneficial effects of this invention are:

[0064] This invention improves the angle estimation performance of radar for low-altitude targets. Under existing technologies, since the true airspace location of a target is unknown beforehand, it's impossible to guarantee that the target will fall within a grid cell when constructing the dictionary matrix. Therefore, when off-grid targets appear, the estimation accuracy of sparse reconstruction algorithms decreases significantly; this is known as the off-grid target problem. This invention introduces a dictionary perturbation δθ to obtain a signal estimation model that more closely approximates the received signal, breaking through the theoretical accuracy limit of existing technologies in estimating off-grid targets and achieving accurate measurement of off-grid targets. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating a sparse reconstruction elevation angle estimation method for off-grid targets provided in an embodiment of the present invention.

[0066] Figure 2 This is a graph showing the root mean square error of the estimation results of the elevation angle of low-altitude targets by the present invention and the traditional sparse reconstruction algorithm as a function of signal-to-noise ratio.

[0067] Figure 3 This is a comparison chart showing the elevation angle estimation results of the present invention and the traditional sparse reconstruction algorithm for 100 independent observations of low-altitude targets. Detailed Implementation

[0068] 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.

[0069] Example 1

[0070] The main idea of ​​this invention is to construct a complete airspace dictionary by utilizing the strong sparsity of the airspace in the elevation angle estimation scenario of meter-wave radar; to add a grid interval to the target estimation model and use it as one of the estimation variables to jointly estimate with the target sparse vector; and then obtain the accurate estimate of the target elevation angle by alternately optimizing and iterating the two estimation variables.

[0071] Please see Figure 1 , Figure 1 This is a flowchart illustrating a sparse reconstruction elevation angle estimation method for off-grid targets provided by an embodiment of the present invention. The embodiment of the present invention provides a sparse reconstruction elevation angle estimation method for off-grid targets, which includes:

[0072] Step 1: The meter-wave array radar transmits an M-dimensional signal to the target within its detection range and then receives the echo signal from the target.

[0073] Specifically, the meter-wave array radar comprises M isotropic array elements arranged at half-wavelength intervals, placed perpendicular to the ground plane. After transmitting an M-dimensional signal to a target within its detection range, the meter-wave array radar receives echo signals from the target. The echo signals from the target include direct echo signals with a path of "target-radar" and multipath echo signals with a path of "target-ground reflection-radar". Since the purpose of this invention is to estimate the elevation angle of the target, the following steps only process the echo signals received by the array radar in the elevation dimension, without considering the echo signals received by the array radar in the azimuth dimension; where M is a positive integer greater than 1.

[0074] Step 2: Perform L digital sampling snapshots on the target's echo signal based on the target range element to obtain L digital sampling snapshot data for M antenna array elements.

[0075] Step 2.1: Determine the target range cell by performing pulse compression processing and moving target detection on the target's echo signal.

[0076] Step 2.2: Perform L digital sampling snapshots on the target echo signal at the target range cell to obtain L digital sampling snapshot data for M antenna elements. The l-th digital sampling snapshot data of the m-th antenna element is denoted as y. m (l), m=1,2,3,…,M, l=1,2,3,…,L, L is a positive integer greater than or equal to 1. Considering that the position information of the aircraft may be updated frequently under high-speed flight, the value of L is generally small.

[0077] Step 3: Obtain the sampling matrix based on the l-th digital sampling snapshot data of the echo from the m-th antenna element. Process the sampling matrix using singular value decomposition (SVD) to obtain the dimension-reduced echo data vector Y. sv After dimensionality reduction, the data was reduced to one dimension while preserving the signal-to-noise ratio gain.

[0078] Step 3.1: Arrange the L-time digital sampling snapshot data of the echo of the m-th antenna element in order to obtain the sampling vector of the echo of the target detected by the m-th antenna element.

[0079] Specifically, based on the l-th digital sampling snapshot data y of the echo of the m-th antenna element... m (l), and let l = 1, 2, 3, ..., L, then we can obtain the first digital sampling snapshot data y of the echo of the m-th antenna element. m (1) The Lth digital sampling snapshot data y of the echo of the m-th antenna element m (L) is denoted as the Lth digitally sampled snapshot data y of the echo of the m-th antenna element. m (1),y m (2),y m (3),...,ym (L).

[0080] The Lth digitally sampled snapshot data y of the echo of the m-th antenna element. m (1),y m (2),y m (3),...,y m (L) Arrange the samples in the following manner to obtain the sampling vector Y of the target echo detected by the m-th antenna element. m :

[0081] Y m =[y m (1),y m (2),y m (3),...,y m (L)].

[0082] Step 3.2: Obtain the sampling matrix composed of the sampling vectors of the M antenna array elements based on the sampling vectors of the echoes detected by the M antenna array elements.

[0083] Specifically, the sampling vector Y of the echo from the m-th antenna element is used. m And let m = 1, 2, 3, ..., M, then we obtain the sampling matrix Y composed of the sampling vectors of the M antenna array elements:

[0084]

[0085] Step 3.3: Perform singular value decomposition on the sampling matrix Y using the singular value decomposition technique, decomposing it into an M×M dimensional left singular matrix U, an M×L dimensional matrix Λ, and an L×L dimensional right singular matrix V. H In this matrix, the diagonal elements are singular values ​​and the remaining elements are 0, i.e.:

[0086] Y = UΛV H

[0087] in,[·] H This indicates the conjugate transpose operation on the matrix.

[0088] Step 3.4: Based on the sampling matrix and the right singular matrix V H and M×1 dimensional column vectors The reduced-dimensional echo data vector is obtained, which is M×1 dimensional. It is an L-1 dimensional zero column vector, that is:

[0089] Y sv =YVT.

[0090] Step 4: Based on the angle search range of the meter-wave array radar and the echo model of the multipath signal, construct the search airspace dictionary and divide the entire search airspace dictionary into J parts, where J>M.

[0091] This includes initializing the search range. This involves determining the angular search range [θ] of the meter-wave array radar. start ,θ end ], θ start θ represents the minimum angle search value of the meter-wave array radar. end This represents the maximum angle search value for a meter-wave array radar, typically taken as θ. end -θ start ≤θ 3dB Generally, the meter-wave array radar is set to point at θ. x If the angle is θ = 0° and parallel to the position, then the angle search range of the meter-wave radar is generally set to θ. start =0° and θ end =θ 3dB Where θ 3dB This represents the beam half-power width of the signal transmitted by the array radar to a target within its detection range. M represents the total number of antenna elements in the meter-wave array radar, d is the spacing between antenna elements, λ represents the carrier wavelength of the signal transmitted by the meter-wave array radar to the target within its detection range, and λ = c / f0, where c represents the speed of light and f0 represents the center frequency of the carrier wave of the signal transmitted by the meter-wave array radar to the target within its detection range.

[0092] Step 4.1: Obtain the direct wave signal data x received by the m-th antenna element. dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t).

[0093] Specifically, since the direct echo signal and the multipath echo signal superimpose within the same range cell, and because the multipath echo signal travels a slightly longer distance and undergoes one reflection, a complex coefficient is needed to describe the path difference between the multipath wave and the direct wave, as well as the loss after ground reflection. Therefore, the direct wave signal data x received by the m-th antenna element... dm (t) can be represented as:

[0094]

[0095] Where s(t) is the transmitted signal of the antenna array element, and n m (t) represents the additive white noise of the m-th antenna element channel, θ d Let d be the elevation angle of the target to be estimated, and d be the spacing between array elements.

[0096] The multipath signal data x received by the m-th antenna element mm (t) can be represented as:

[0097]

[0098] Where, θ s Let ρ be the multipath elevation angle of the target, ρ be the reflection coefficient, α = 2πΔR / λ be the phase difference between the direct wave and the multipath wave due to time delay, and ΔR be the path difference between the direct wave and the multipath wave.

[0099] Step 4.2: The direct wave signal data x received by the m-th antenna element... dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t) are superimposed to obtain the composite data x received by the m-th antenna element. m (t), and combine the composite data x m (t) is denoted as the echo model of the multipath signal, and the composite data x m (t) is:

[0100]

[0101] Step 4.3: Based on the composite data x received by the M antenna elements m (t) Obtain the composite data x of M antenna elements m The sampling matrix X(t) is formed by (t), and the sampling matrix X(t) is:

[0102]

[0103] Among them, complex variables This describes the total multipath loss, with column vector N(t) = [n1(t),...,n m (t)] T This describes the additive white noise of M array element channels, where a(·) represents the steering vector at the corresponding angle under the manifold of the radar array, and a(θ) d ) is the steering vector of the target elevation angle to be estimated under this radar array manifold, a(θ) s The multipath elevation angle of the target is the steering vector under the radar array manifold.

[0104] Step 4.4: Obtain the composite steering vector Φ based on the sampling matrix X(t). a (θ j ).

[0105] Specifically, using composite data x from M antenna elements m Given the sampling matrix X(t) composed of (t), if the current site is a classic planar multipath scenario and the height difference hr from the array center to the reflector is known, the classical site prior can be obtained based on the geometric relationship between the radar, target, and reflector in the classical multipath signal model. The atom in the dictionary is defined as a composite steering vector containing both the direct wave steering vector and the multipath steering vector, representing the signal received by the target at the corresponding elevation angle. The atom is defined as follows:

[0106]

[0107] Where, Φ a To search the spatial domain dictionary, θ j To search for the pitch angle corresponding to the j-th atom in the spatial domain dictionary, a(θ) j ) represents the pitch angle θ j The steering vector Φ under the manifold of this radar array a (θ j ) represents the target in a(θ) j The steering vector is the composite steering vector for receiving signals when the steering vector represents the direction.

[0108] Step 4.5: Search range based on angle [θ] start ,θ end ], with a fixed search interval The entire spatial domain is discretized into J grids, and the atomic vector of each grid is the corresponding Φ. a (θ j If ), then search the spatial domain dictionary Φ a Represented as an M×J dimensional matrix:

[0109]

[0110] Where, Φ a To search the spatial domain dictionary, a(θ) start ) represents the steering vector for finding the minimum angle of the meter-wave array radar under the radar array manifold, a(θ) end ) is the steering vector for the maximum angle search value of the meter-wave array radar under the radar array manifold.

[0111] Step 5: Based on the dimension-reduced echo data vector and the search spatial dictionary, use the orthogonal matching pursuit algorithm to make a preliminary estimate of the target's elevation angle, and obtain the initial estimated elevation angle of the target and the sparse coefficient vector of the corresponding K targets.

[0112] Step 5.1: Select the residual e with respect to the current iteration number k. k The dictionary atom with the largest inner product is added to the current support index set to obtain the updated support index set.

[0113] By replacing the solution with the l0-norm solution under the l1-norm condition, and constraining the solution results with an error similarity, the problem of solving the elevation angle can be sparsely represented as follows:

[0114]

[0115] Where, θ k γ is the estimated elevation angle of the k-th target. k Let a(θ) be the target k. k The sparse coefficients in the direction of ) and the sparse coefficient vector γ of the K targets. (1) By γ k Composition, i.e., γ (1) =[γ1,γ2,...,γ k ] (1) Initialize the sparse coefficients of all atoms to 0.

[0116] Define η k For the k-th iteration [θ start ,θ end The sparse vector consisting of the sparse coefficients of all atoms within the [equation], and the residual e k The error at the k-th iteration is e. k =Y sv -Φ a η k Initialize residual e0 = Y sv Define the supporting index set as the structure of the received dimensionality-reduced signal Y. sv The dictionary's atomic set, initialized with an empty supporting index set, i.e. The prior sparsity of the algorithm is K, representing that the received signal Y consists of a total of K target echoes. sv .

[0117] Choose the residual e with respect to the current iteration number k. k The atom with the largest inner product:

[0118]

[0119] Where, λ k Let be the dictionary atoms selected for the k-th iteration, `<·,·>` represent the inner product of two vectors, and `|·|` represent the absolute value. Add the found relevant elements to the current support index set.

[0120] Γ k+1 =Γ k ∪{λ k}

[0121] Where ∪ represents the union operation of sets, and Γ represents the union operation of sets. k Γ is the support index set corresponding to the k-th iteration. k+1 This is the support index set corresponding to the (k+1)th iteration.

[0122] Step 5.2: Based on the updated support index set Γ k+1 Combined into matrix Φ Γk+1 Then the orthogonal projection operator P of this atomic space is:

[0123]

[0124] in,[·] T For the transpose operation of a matrix, [·] -1 This is the operation for finding the inversion of a matrix.

[0125] By from residual e k Subtract its in The updated residual e is obtained by the orthogonal projection onto the spanned space. k+1 e k+1 =e k -Pe k ;

[0126] Record the sparse coefficient γ corresponding to the selected dictionary atom. k =Pe k .

[0127] Step 5.3: Let k = k + 1. At this point, a complete iteration is completed. Return to step 5.1 until the iteration exit requirement k = K is met.

[0128] Step 5.4: Obtain the elevation angle estimates corresponding to K targets based on the dictionary atoms in the support index set after iteration, and obtain the sparse coefficient vector of K targets for the orthogonal matching tracking algorithm based on the sparse coefficients.

[0129] The estimated elevation angles for the K targets are:

[0130] θ (1) =[θ1,θ2,θ3,...,θ K ] (1)

[0131] Among them, the elevation angle estimation of the k-th target To support the spatial position of the k-th atom in the index set;

[0132] The sparse coefficient vector of the K targets is:

[0133] γ (1) =[γ1,γ2,γ3,...,γ K ] (1)

[0134] Wherein, the sparsity coefficient γ of the k-th objective k =Pe k .

[0135] Step 6: Based on the initial estimated elevation angle and sparse coefficient vector of the target, the estimates of the grid perturbation and the target sparse vector are updated by alternating iteration. The grid points are updated to the true elevation angle position of the target through grid perturbation, thereby obtaining the estimated elevation angle of the target.

[0136] Specifically, a grid perturbation δθ is added to the sparse reconstruction model to form a new signal estimation model, which is then jointly estimated with the target sparse vector γ, using the estimation result θ from step 5. (1) With γ (1) As initial values, the estimates of unknowns δθ and γ are updated by alternating iteration. The grid points are updated to the true elevation angle position of the target by grid perturbation, thereby obtaining the elevation angle estimate of the target. The elevation angle estimate of the target is the sparse reconstruction elevation angle estimate result for off-grid targets.

[0137] Step 6.1: Introduce the mesh perturbation δθ. When the sparsity is K, the mesh perturbation is:

[0138] δθ=[δθ1, δθ2, δθ3,..., δθ K ]

[0139] Where, δθ k The k-th target is the nearest point in the original dictionary grid, θ. k Unknown disturbances.

[0140] Step 6.2: Obtain the estimation model based on the grid perturbation δθ and the target sparse vector γ.

[0141] By adding δθ to the target estimation model, it is used as one of the estimation variables and jointly estimated with the target sparse vector γ. Therefore, the new estimation model can be written as:

[0142]

[0143] Among them, Y sv The received echo signal; k is the target number, K is the number of targets; γ k Φ represents the sparse coefficients of the k-th target, signifying the signal strength; a For a dictionary, where δθ k The distance θ represents the distance of the k-th target to the nearest original grid point in the dictionary. k The unknown disturbance, therefore Φ a (θ k +δθ k This represents the atomic vector that falls at the true location of the k-th target after perturbation. In the constraints, Δ represents the interval of the original dictionary, meaning the perturbation cannot exceed half the interval of the original dictionary. To obtain the most accurate estimate of the received signal Y, the above formula is used to jointly estimate the perturbation values ​​and sparse coefficients of the original dictionary grid points, thus achieving precise measurement of off-grid targets.

[0144] Step 6.3: Let t = 1, where t is the current iteration number, and T maxTo determine the maximum number of iterations for the algorithm, the initial value of the sparse vector of the K targets is the sparse coefficient vector γ obtained in step 5. (1) The initial elevation angle estimates for the K targets are the initial estimated elevation angles θ obtained in step 5. (1) .

[0145] Step 6.4: Keep the sparse vectors of the K targets unchanged, and optimize the grid perturbation based on the estimation model.

[0146] Specifically, a sparse vector of fixed K targets. Keep it unchanged, optimize the perturbation amount The objective function to be optimized is:

[0147]

[0148] The model in the above equation is consistent with the least squares problem, but it is no longer linear. Solving nonlinear problems introduces significant computational complexity. Therefore, a linear optimization solution is performed on the above equation. For the nonlinear part... Expanding to the first term using a Taylor series, it can be rewritten as:

[0149]

[0150] Therefore, the objective function can be rewritten as:

[0151]

[0152] Where ζ=[δθ1,...,δθ K Let ] be a K×1 vector recording the perturbation, and [·]′ be the derivative of the matrix vector. The objective function is now a standard least squares problem with a closed-form solution.

[0153] Step 6.5: Based on the dimension-reduced echo data vector and the sparse vector γ of the K targets in the t-th iteration... (t) The data residual for the t-th iteration is obtained by combining the corresponding dictionary atoms. Data residuals for:

[0154]

[0155] Step 6.6: Take the partial derivative θ with respect to the variables of each dictionary atom of the K targets in the t-th iteration. k The partial derivatives are obtained, and the partial derivative dictionary matrix A is obtained based on the partial derivatives. (t) .

[0156] Specifically, based on the dictionary atoms of the K targets in the t-th iteration... Calculate the relationship between each dictionary atom and its variable θ k Find the partial derivative, denoted as

[0157]

[0158] The partial derivative dictionary matrix A is calculated based on the obtained partial derivative results and the sparse vector of the target. (t) :

[0159]

[0160] Step 6.7: Based on the data residuals And partial derivative dictionary matrix A (t) Obtain the new objective function This yields the mesh perturbation amount for the t-th iteration.

[0161] Specifically, the rewritten objective function This is a standard least squares problem with a closed-form solution. The result of calculating the closed-form solution is as follows:

[0162]

[0163] Since the perturbation of the grid points in the dictionary must be a real value, the dictionary perturbation in the t-th iteration is taken as:

[0164]

[0165] Where Re{·} represents the real value of the corresponding vector.

[0166] Step 6.8: Obtain the updated dictionary grid point positions based on the grid perturbation amount in the t-th iteration, i.e.:

[0167]

[0168] Step 6.9: Keep the dictionary grid positions of the K targets unchanged, optimize the sparse vector of the K targets using the optimization objective function, and obtain the update matrix B based on the updated dictionary grid positions. (t+1) .

[0169] Specifically, the dictionary grid positions of K targets are fixed. Without changing the target, optimize the sparse vector of K targets. The objective function to be optimized is:

[0170]

[0171] The above formula is consistent with the model of the least squares solution problem of the form AX = b. The lattice points θ are updated based on the updated dictionary. (t+1) The update matrix B is calculated. (t+1) Update the dictionary atoms corresponding to the lattice points:

[0172]

[0173] Step 6.10: Based on the update matrix B (t+1) Based on the closed-form solution of the linear least squares solution, the updated sparse vector of the K objectives is obtained, i.e.:

[0174] γ (t+1) =((B) (t+1) ) H B (t+1) ) -1 (B (t+1) ) H Y sv .

[0175] Step 6.11: Let t = t + 1, and determine whether t = T. max If so, then stop iterating; the dictionary grid position at this point is... This refers to the elevation angle estimates corresponding to K targets. The signal strengths are the values ​​corresponding to the K targets. If not, return to step 6.4 until t = T. max .

[0176] This invention proposes a sparse reconstruction elevation angle estimation method for off-grid targets. This method directly solves the off-grid problem in the discrete parameter space, that is, by adding a perturbation term to a pre-defined grid, it achieves accurate estimation of off-grid targets. This method can reduce the elevation angle estimation error for low-altitude targets and improve the radar's angle estimation performance for low-altitude targets.

[0177] The effects of this invention are further illustrated by the following simulation experiments:

[0178] 1. Simulation conditions

[0179] Default parameters: The linear array has 16 elements, the operating wavelength is 1m, the element spacing is half the operating wavelength, the radar array center is 30m above the reflector, the target range is 100km, the multipath reflection coefficient is -0.9, and the multipath wave incident angle is θ. s =-θ d The number of snapshots was 1, and the noise followed a complex Gaussian random distribution with a mean of zero. Multiple Monte Carlo experiments were conducted independently, and the root mean square error (RMSE) of the experimental results was calculated according to the following formula to measure the performance of angle estimation.

[0180]

[0181] Where N is the number of independent Monte Carlo trials, θ d Let be the true value of the target elevation angle. This represents the result of the i-th Monte Carlo experiment.

[0182] 2. Simulation Content

[0183] Simulation 1: When the target's true elevation angle is 2.7°, the elevation angle is estimated using both the traditional Orthogonal Matching Pursuit (OMP) algorithm and the method of this invention. The OMP algorithm's dictionary is set with a grid interval of 0.2°. One hundred Monte Carlo experiments were conducted independently, and the root mean square error of the angle estimate as a function of the signal-to-noise ratio was obtained, as shown in the figure. Figure 2 As shown.

[0184] Simulation 2: The dictionary settings for the orthogonal matching pursuit algorithm are a grid interval of 0.2° and an echo signal-to-noise ratio of 20dB. The elevation angle of the target is estimated using both the algorithm of this invention and the traditional orthogonal matching pursuit algorithm. One hundred Monte Carlo experiments are conducted independently, and the estimation results from the 100 Monte Carlo experiments are shown below. Figure 3 As shown.

[0185] 3. Simulation Analysis

[0186] from Figure 2 As can be seen, when the target's elevation angle is 2.7°, the angle estimation error of this invention is smaller than that of the traditional orthogonal matching tracking algorithm. The target elevation angle of 2.7° does not fall on a dictionary grid point, and the nearest grid point is θ. i =2.6° and θ i =2.8°, therefore, the theoretical accuracy limit of the traditional orthogonal matching pursuit algorithm should be RMSE = 0.1°. From Figure 2 It can be seen that when the signal-to-noise ratio reaches 20dB, the estimation performance of the traditional orthogonal matching pursuit algorithm reaches its limit and can no longer break through the theoretical accuracy limit caused by off-net targets. However, the algorithm of this invention breaks through the theoretical accuracy limit at around 15dB and can obtain better estimation performance.

[0187] from Figure 3 It can be more clearly seen that, under a signal-to-noise ratio of 20dB, the angle measurement results of the OMP algorithm mostly converge to 2.6° and 2.8°, while the Off-Grid algorithm can converge to around 2.7° near the true target position.

[0188] Simulation experiments show that for low-altitude targets, the angle estimation performance of this invention is significantly better than that of the traditional orthogonal matching tracking algorithm, reducing the angle estimation error and providing the ability to detect off-grid targets when using sparse reconstruction algorithm to measure elevation angle for meter-wave radar.

[0189] In conclusion, the simulation experiments verified the correctness, effectiveness, and reliability of the present invention.

[0190] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0191] Although this application has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings, disclosure, and appended claims, will understand and implement other variations of the disclosed embodiments in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0192] 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 sparse reconstruction elevation angle estimation method for off-grid targets, characterized in that, The sparse reconstruction elevation angle estimation method includes: Step 1: The meter-wave array radar transmits an M-dimensional signal to the target within its detection range and then receives the echo signal from the target. Step 2: Perform L digital sampling snapshots on the echo signal of the target based on the target range element to obtain L digital sampling snapshot data of M antenna array elements; Step 3: Obtain the sampling matrix based on the l-th digital sampling snapshot data of the echo of the m-th antenna array element, and process the sampling matrix using singular value decomposition to obtain the dimension-reduced echo data vector, where 0 < m ≤ M; Step 4: Based on the angle search range and multipath signal echo model of the meter-wave array radar, construct the search airspace dictionary and divide the entire search airspace dictionary into J parts, where J>M; Step 5: Based on the dimension-reduced echo data vector and the search spatial domain dictionary, the orthogonal matching pursuit algorithm is used to make a preliminary estimate of the target's elevation angle, and the initial estimated elevation angle of the target and the sparse coefficient vector of the corresponding K targets are obtained. Step 6: Based on the initial estimated elevation angle and sparse coefficient vector of the target, the estimates of the grid perturbation and the target sparse vector are updated by alternating iteration. The grid points are updated to the true elevation angle position of the target through grid perturbation, thereby obtaining the estimated elevation angle of the target.

2. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, The meter-wave array radar comprises M isotropic array elements arranged at half-wavelength intervals, placed perpendicular to the ground plane.

3. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, Step 2 includes: Step 2.1: By performing pulse compression processing and moving target detection on the echo signal of the target, the target range cell where the target is located is determined; Step 2.2: Perform L digital sampling snapshots on the echo signal of the target at the target range unit to obtain L digital sampling snapshot data of the M antenna array elements.

4. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, Step 3 includes: Step 3.1: Arrange the L digital sampling snapshot data of the echo of the m-th antenna element in order to obtain the sampling vector of the echo of the target detected by the m-th antenna element; Step 3.2: Obtain the sampling matrix composed of the sampling vectors of the M antenna array elements based on the sampling vectors of the echoes detected by the M antenna array elements. Step 3.3: Perform singular value decomposition on the sampling matrix using singular value decomposition (SVD) technology, decomposing it into an M×M dimensional left singular matrix U, an M×L dimensional matrix Λ, and an L×L dimensional right singular matrix V. H In this matrix Λ, the diagonal elements are singular values ​​and the remaining elements are 0; Step 3.4: Based on the sampling matrix and the right singular matrix V H and M×1 dimensional column vectors The reduced-dimensional echo data vector is obtained. It is an L-1 dimensional zero column vector.

5. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, The meter-wave array radar has an angle search range of [θ]. start ,θ end ], θ start θ represents the minimum angle search value of the meter-wave array radar. end θ represents the maximum angle search value of the meter-wave array radar, where θ end -θ start ≤θ 3dB θ 3dB This represents the beam half-power width of the signal transmitted by the meter-wave array radar to a target within its detection range.

6. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 5, characterized in that, Step 4 includes: Step 4.1: Obtain the direct wave signal data x received by the m-th antenna element. dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t); The direct wave signal data x dm (t) is: Where s(t) is the transmitted signal of the antenna array element, and n m (t) represents the additive white noise of the m-th antenna element channel, θ d The pitch angle of the target to be estimated; The multipath wave signal data x mm (t) is: Where, θ s Let ρ be the multipath elevation angle of the target, ρ be the reflection coefficient, α = 2πΔR / λ be the phase difference between the direct wave and the multipath wave due to time delay, and ΔR be the path difference between the direct wave and the multipath wave. Step 4.2: The direct wave signal data x received by the m-th antenna element... dm (t) and the multipath wave signal data x received by the m-th antenna element mm (t) are superimposed to obtain the composite data x received by the m-th antenna element. m (t), and combine the composite data x m (t) is denoted as the echo model of a multipath signal; Step 4.3: Based on the composite data x received by the M antenna elements m (t) Obtain the composite data x of M antenna elements m The sampling matrix X(t) is composed of (t); Step 4.4: Obtain the composite steering vector Φ based on the sampling matrix X(t). a (θ j The composite guiding vector Φ a (θ j )for: Where, Φ a To search the spatial domain dictionary, θ j To search for the pitch angle corresponding to the j-th atom in the spatial domain dictionary, a(θ) j ) represents the pitch angle θ j The steering vector Φ under the manifold of this radar array a (θ j ) represents the target in a(θ) j The steering vector represents the composite steering vector of the received signal when the direction is represented, and hr is the height difference from the center of the array to the reflective surface; Step 4.5: Based on the angle search range [θ] start ,θ end ], with a fixed search interval The entire spatial domain is discretized into J grids, and the atomic vector of each grid is the corresponding Φ. a (θ j If ), then search the spatial domain dictionary Φ a Represented as an M×J dimensional matrix: Where, Φ a To search the spatial domain dictionary, a(θ) start ) represents the steering vector for finding the minimum angle of the meter-wave array radar under the radar array manifold, a(θ) end ) is the steering vector for the maximum angle search value of the meter-wave array radar under the radar array manifold.

7. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, Step 5 includes: Step 5.1: Select the residual e with respect to the current iteration number k. k The dictionary atom with the largest inner product is added to the current support index set to obtain the updated support index set. The dictionary atom is: Where, λ k Let be the dictionary atom selected for the k-th iteration, <·,·> be the inner product of two vectors, and |·| be the absolute value; Step 5.2: Combine the updated support index set into a matrix. Then the orthogonal projection operator P of this atomic space is: in,[·] T For the transpose operation of a matrix, [·] -1 This is the operation for finding the inversion of a matrix. By from residual e k Subtract its in The updated residual e is obtained by the orthogonal projection onto the spanned space. k+1 e k+1 =e k -Pe k ; The sparsity coefficient corresponding to the selected dictionary atom is γ. k =Pe k ; Step 5.3: Let k = k + 1. At this point, a complete iteration is completed. Return to step 5.1 until the iteration exit requirement k = K is met. Step 5.4: Obtain the elevation angle estimates corresponding to K targets based on the dictionary atoms in the support index set after iteration, and obtain the sparse coefficient vector of K targets for the orthogonal matching tracking algorithm based on the sparse coefficients.

8. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, characterized in that, Step 6 includes: Step 6.1: Introduce the mesh perturbation δθ. When the sparsity is K, the mesh perturbation is: δθ=[δθ1,δθ2,δθ3,...,δθ K ] Where, δθ k The k-th target is the nearest point in the original dictionary grid, θ. k Unknown disturbances; Step 6.2: Obtain the estimation model based on the grid perturbation δθ and the target sparse vector γ; Step 6.3: Let t = 1, where t is the current iteration number, and T max To determine the maximum number of iterations for the algorithm, the initial value of the sparse vector of the K targets is the sparse coefficient vector γ obtained in step 5. (1) The initial elevation angle estimates for the K targets are the initial estimated elevation angles θ obtained in step 5. (1) ; Step 6.4: Keep the sparse vectors of the K targets unchanged, and optimize the mesh perturbation based on the estimation model; Step 6.5: Based on the dimension-reduced echo data vector and the sparse vector γ of the K targets in the t-th iteration... (t) The data residual for the t-th iteration is obtained by combining the corresponding dictionary atoms. Step 6.6: Take the partial derivative θ with respect to the variables of each dictionary atom of the K targets in the t-th iteration. k The partial derivatives are obtained, and the partial derivative dictionary matrix A is obtained based on the partial derivatives and the sparse vector of the target. (t) ; Step 6.7: Based on the data residuals And partial derivative dictionary matrix A (t) Obtain the new objective function This yields the mesh perturbation amount for the t-th iteration; Step 6.8: Obtain the updated dictionary grid point positions based on the grid perturbation amount in the t-th iteration; Step 6.9: Keep the dictionary grid positions of the K targets unchanged, optimize the sparse vector of the K targets using the optimization objective function, and obtain the update matrix B based on the updated dictionary grid positions. (t+1) ; Step 6.10: Based on the update matrix B (t+1) Based on the closed-form solution of the linear least squares solution, the updated sparse vector of the K objectives is obtained; Step 6.11: Let t = t + 1, and determine whether t = T. max If yes, stop iterating; the dictionary grid positions at this point are the elevation angle estimates for the K targets. If no, return to step 6.4 until t = T. max .

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