CN116338618A - Sparse reconstruction elevation angle estimation method for off-grid targets - Google Patents
Sparse reconstruction elevation angle estimation method for off-grid targets Download PDFInfo
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Abstract
The invention discloses a sparse reconstruction elevation angle estimation method for an off-grid target, which is characterized by comprising the following steps of: performing L times of digital sampling snapshot on the echo signals of the target based on the target distance unit to obtain L times of digital sampling snapshot data of M antenna array elements; processing the sampling matrix by a singular value decomposition technology to obtain echo data vectors after dimension reduction; constructing a search airspace dictionary, and dividing the whole search airspace dictionary into J parts; performing preliminary estimation on the elevation angle of the target by using an orthogonal matching pursuit algorithm to obtain initial estimated elevation angles of the target and sparse coefficient vectors of K corresponding targets; based on the initial estimated elevation angle of the target and the sparse coefficient vector, updating the estimation of the grid disturbance quantity and the sparse vector of the target through an alternate iteration method, updating the grid point to the real elevation angle position of the target through grid disturbance, and further obtaining the elevation angle estimated value of the target. The invention improves the angle estimation performance of the radar on the low-altitude target.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a sparse reconstruction elevation angle estimation method for an off-grid target, which is suitable for elevation angle estimation of a meter wave radar on a low-altitude target.
Background
With the development of the flight technology of aircrafts in recent years, the accuracy requirements of radar on target detection means are becoming urgent. However, since the beam of the meter wave radar is wide, when the low-altitude motion of the target is detected, the high-coherence direct wave signal and the multi-path reflected signal are simultaneously received by the radar receiving array from the same beam, and the elevation estimation performance of the meter wave radar is seriously affected. Therefore, how to improve the low elevation target measurement performance of the meter wave radar is one of the key problems that make the meter wave radar have more excellent performance.
In recent years, the super-resolution algorithm based on the array signal is applied to elevation angle estimation of the meter wave radar, and is more typical of sparse reconstruction type algorithms, and the method has the greatest advantages that the number of information sources is not required to be known, the method is not influenced by coherence, good pitch angle estimation accuracy can be obtained under the condition of fewer snapshots, the problem that the characteristic subspace type algorithm has too high requirement on the snapshots is solved, and an effective solution idea is provided for meeting the real-time performance of a low elevation angle measurement scene. However, the disadvantage is that the sparse reconstruction algorithm estimates by dividing a plurality of grids for the airspace to form a dictionary, and only the nearest grid points can be approximated to the grid targets which do not fall on the grid points, which leads to a large accuracy limitation on elevation angle estimation of the grid targets.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a sparse reconstruction elevation angle estimation method for an off-grid target. The technical problems to be solved by the invention are realized by the following technical scheme:
an off-grid target-oriented sparse reconstruction elevation angle estimation method, comprising:
step 1, a meter wave array radar transmits signals of M dimensions to a target in a detection range of the meter wave array radar and then receives echo signals from the target;
step 4, constructing a search airspace dictionary based on the angle search range of the meter wave array radar and an echo model of the multipath signal, and dividing the whole search airspace dictionary into J parts, wherein J is greater than M;
step 5, based on the echo data vector after dimension reduction and a search airspace dictionary, carrying out preliminary estimation on the elevation angle of the target by utilizing an orthogonal matching pursuit algorithm to obtain initial estimated elevation angles of the target and sparse coefficient vectors of the K corresponding targets;
and 6, updating the estimation of the grid disturbance quantity and the target sparse vector by an alternate iteration method based on the initial estimated elevation angle and the sparse coefficient vector of the target, updating the grid point to the real elevation angle position of the target by the grid disturbance, and further obtaining the elevation angle estimation value of the target.
In one embodiment of the invention, the meter wave array radar comprises M isotropic array elements arranged at half-wavelength intervals and placed perpendicular to the array ground plane.
In one embodiment of the present invention, the step 2 includes:
step 2.1, determining a target distance unit where the target is located by performing pulse compression processing and moving target detection on the echo signal of the target;
and 2.2, carrying out L times of digital sampling snapshot on the echo signals of the target at the target distance unit to obtain L times of digital sampling snapshot data of the M antenna array elements.
In one embodiment of the present invention, the step 3 includes:
step 3.1, arranging the L times of digital sampling snapshot data of the echo of the mth antenna array element according to the sequence to obtain a sampling vector of the echo of the mth antenna array element detection target;
step 3.2, obtaining a sampling matrix formed by sampling vectors of M antenna array elements according to the sampling vectors of echoes of the detection targets of the M antenna array elements;
step 3.3, performing singular value decomposition on the sampling matrix by a singular value decomposition technology, wherein the singular value decomposition is decomposed into a matrix lambda of a left singular matrix U, M xL of M x M dimensions and a right singular matrix V of L x L dimensions H Wherein the diagonal of the matrix Λ is a singular value and the rest elements are 0;
step 3.4, according to the sampling matrix and the right singular square matrix V H And M x 1-dimensional column vectors
Obtaining echo data vector after dimension reduction, < + >>
Is a zero column vector of L-1 dimension.
In one embodiment of the invention, the meter wave array radar angle search range is [ theta ] start ,θ end ]，θ start Representing the minimum value, theta, of the angle search of the meter wave array radar end Representing an angle search maximum of the meter wave array radar, wherein θ end -θ start ≤θ 3dB ，θ 3dB And the half-power width of the wave beam of the target transmitting signals of the detection range of the meter wave array radar is represented.
In one embodiment of the present invention, the step 4 includes:
step 4.1, obtaining direct wave signal data x received by an mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t)；
The direct wave signal data x dm (t) is:
wherein s (t) is the transmitting signal of the antenna array element, n m (t) is the additive white noise of the m-th antenna element channel, θ d The pitch angle is a target pitch angle to be estimated;
the multipath wave signal data x mm (t) is:
wherein θ s As the multipath pitch angle of the target, ρ is a reflection coefficient, α=2pi Δr/λ is the phase difference between the direct wave and the multipath wave due to time delay, and Δr is the wave path difference between the direct wave and the multipath wave;
step 4.2, direct wave signal data x received by the mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t) superposing to obtain composite data x received by the mth antenna array element m (t) and combining the data x m (t) an echo model of the multipath signal;
step 4.3, according to the composite data x received by M antenna array elements m (t) obtaining composite data x of M antenna array elements m A sampling matrix X (t) constituted by (t);
step 4.4, obtaining a composite steering vector phi according to the sampling matrix X (t) a (θ j ) The composite steering vector phi a (θ j ) The method comprises the following steps:
wherein phi is a To search the airspace dictionary, θ j To search for a pitch angle, a (θ j ) Is the pitch angle theta j Steering vector, Φ, under the radar array manifold a (θ j ) Representative target is represented by a (θ) j ) The steering vector represents the composite steering vector of the received signal, hr is the height difference from the center of the array to the reflecting surface;
step 4.5, searching for the range [ θ ] based on the angle start ,θ end ]At fixed search intervals
Dispersing the whole airspace into J-shaped grids, wherein the atomic vector of each grid is corresponding phi a (θ j ) Searching the airspace dictionary phi a Matrix expressed as M x J dimensions:
wherein phi is a To search the spatial dictionary, a (θ start ) Searching for a steering vector, a (θ) end ) The steering vector of the maximum under the radar array manifold is searched for the angle of the meter wave array radar.
In one embodiment of the present invention, the step 5 includes:
step 5.1, selecting the residual error e with the current iteration number k k Adding the dictionary atom with the largest inner product into the current support index set to obtain an updated support index set, wherein the dictionary atom is as follows:
wherein lambda is k The dictionary atoms selected for the kth iteration,<·,·>for the inner product of two vectors, |·| is the absolute value;
step 5.2, combining the support index sets into a matrix according to the updated support index sets
The orthogonal projection operator P of this atomic space is then:
wherein [ (S)] T For transpose operation of matrix, [. Cndot.] -1 Inversion operation for the matrix;
by slave ofResidual e k Subtracting it from
The orthographic projection on the stretched space obtains updated residual error e k+1 ，e k+1 ＝e k -Pe k ；
The selected dictionary atom corresponds to a sparse coefficient of gamma k ＝Pe k ；
Step 5.3, let k=k+1, finish a complete iteration at this moment, return to step 5.1, until reaching the iteration and withdrawing the requirement k=k;
and 5.4, obtaining elevation angle estimation corresponding to the K targets according to dictionary atoms in the support index set after iteration, and obtaining sparse coefficient vectors of the K targets of the orthogonal matching pursuit algorithm according to the sparse coefficients.
In one embodiment of the present invention, the step 6 includes:
step 6.1, introducing grid disturbance delta theta, and when the sparsity is K, obtaining the grid disturbance delta theta as follows:
δθ＝[δθ 1 ,δθ 2 ,δθ 3 ,...,δθ K ]
wherein δθ k Original grid point theta of nearest dictionary for kth target distance k Unknown disturbance of (a);
step 6.2, obtaining an estimation model according to the grid disturbance delta theta and the target sparse vector gamma;
step 6.3, let t=1, where T is the current iteration number, T max For the maximum iteration times of the algorithm, the initial values of the sparse vectors of the K targets are the sparse coefficient vector gamma obtained in the step 5 (1) The initial elevation angle estimation values of the K targets are the initial target estimated elevation angle theta obtained in the step 5 (1) ；
Step 6.4, fixing the sparse vectors of the K targets unchanged, and optimizing grid disturbance quantity based on an estimation model;
step 6.5, according to the echo data vector after dimension reduction and the sparse vector gamma of K targets of the t-th iteration (t) Obtaining the data residual error of the t-th iteration by corresponding dictionary atoms
Step 6.6, solving the bias derivative theta of the variables of each dictionary atom of the K targets of the t-th iteration k Obtaining a partial guide result, and obtaining a partial guide dictionary matrix A according to the partial guide result and the sparse vector of the target (t) ；
Step 6.7, according to the data residual error
Partial guide dictionary matrix A (t) Get new objective function->
Thereby obtaining the grid disturbance quantity of the t-th iteration;
step 6.8, obtaining updated dictionary lattice point positions according to the grid disturbance quantity of the t-th iteration;
step 6.9, fixing the dictionary lattice point positions of the K targets unchanged, optimizing sparse vectors of the K targets by using an optimization objective function, and obtaining an update matrix B according to the updated dictionary lattice point positions (t+1) ；
Step 6.10, based on update matrix B (t+1) Obtaining updated sparse vectors of K targets according to a closed solution of the linear least square solution;
step 6.11, let t=t+1, determine if t=t max If yes, stopping iteration, wherein the dictionary lattice point positions are elevation angle estimates corresponding to K targets, otherwise, returning to step 6.4 until t=T max 。
The invention has the beneficial effects that:
the angle estimation performance of the radar on the low-altitude target is improved. On the basis of the prior art, since the real airspace position of the target is unknown in advance, the target cannot be guaranteed to fall on a grid when constructing a dictionary matrix. Therefore, when off-grid targets occur, the estimation accuracy of the sparse reconstruction type algorithm also drops significantly, which is called off-grid target problem. The method introduces dictionary disturbance delta theta to obtain a signal estimation model which is closer to the received signal, breaks through the theoretical precision limit of the prior art when estimating the off-grid target, and realizes the accurate measurement of the off-grid target.
Drawings
Fig. 1 is a schematic flow chart of a sparse reconstruction elevation angle estimation method for off-grid targets provided by an embodiment of the invention;
FIG. 2 is a graph of the root mean square error versus signal to noise ratio for low altitude target elevation estimation results for the present invention versus a conventional sparse reconstruction algorithm;
FIG. 3 is a graph comparing the results of 100 independent observations of elevation estimates of a low-altitude target with a conventional sparse reconstruction algorithm.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
Example 1
The main idea of the invention is as follows: constructing a complete airspace dictionary by utilizing strong sparsity of airspace under a meter wave radar elevation angle estimation scene; and adding a grid interval into the target estimation model, carrying out joint estimation on one of the estimated variables and the target sparse vector, and obtaining an accurate estimated value of the target elevation angle through alternately optimizing and iterating the two estimated variables.
Referring to fig. 1, fig. 1 is a flow chart of a sparse reconstruction elevation estimation method for off-grid targets according to an embodiment of the present invention. The embodiment of the invention provides a sparse reconstruction elevation angle estimation method for an off-grid target, which comprises the following steps of:
and step 1, transmitting an M-dimensional signal to a target in a detection range by the meter wave array radar, and then receiving an echo signal from the target.
Specifically, the meter wave array radar comprises M isotropic array elements which are distributed at half-wavelength intervals and are placed perpendicular to an array ground plane, the meter wave array radar transmits signals of M dimensions to a target in a detection range of the array ground plane and then receives echo signals from the target, and the echo signals of the target comprise direct echo signals with a path of 'target-radar' and multipath echo signals with a path of 'target-array ground reflection-radar'; because the invention aims to estimate the elevation angle of a target, the following steps only process echo signals received by the pitch dimension of the array radar, and do not consider echo signals received by the direction dimension of the array radar; wherein M is a positive integer greater than 1.
And step 2, carrying out L times of digital sampling snapshot on the echo signals of the target based on the target distance unit to obtain L times of digital sampling snapshot data of M antenna array elements.
And 2.1, determining a target distance unit where the target is located by performing pulse compression processing and moving target detection on the echo signal of the target.
Step 2.2, performing L times of digital sampling snapshot on the echo signals of the target at the target distance unit to obtain L times of digital sampling snapshot data of M antenna array elements, wherein the first times of digital sampling snapshot data of the M antenna array elements are recorded as y m (l) M=1, 2,3, …, M, l=1, 2,3, …, L is a positive integer greater than or equal to 1, and the value of L is generally smaller considering that the position information of an aircraft may be frequently updated under high-speed flight.
And 3.1, arranging the L times of digital sampling snapshot data of the echo of the m-th antenna array element according to the sequence to obtain a sampling vector of the echo of the m-th antenna array element detection target.
Specifically, the data y is snapshot based on the first digital sampling of the mth antenna array element echo m (l) Let l=1, 2,3, …, L, and further obtain the 1 st digital sampling snapshot data y of the m-th antenna array element echo m (1) The L-th digital sampling snapshot data y of the echoes of the mth antenna array element m (L) L times of digital sampling snapshot data y recorded as the echo of the m-th antenna array element m (1),y m (2),y m (3),...,y m (L)。
Sampling the L times of the echo of the m-th antenna array element into snapshot data y m (1),y m (2),y m (3),...,y m (L) arranging in the following manner to obtain a sampling vector Y of the echo of the detection target of the mth antenna array element m ：
Y m ＝[y m (1),y m (2),y m (3),...,y m (L)]。
And 3.2, obtaining a sampling matrix formed by sampling vectors of M antenna array elements according to the sampling vectors of echoes of the target detected by the M antenna array elements.
Specifically, the sampling vector Y of the echo of the mth antenna element is utilized m Let m=1, 2,3, …, M, and further obtain a sampling matrix Y composed of sampling vectors of M antenna elements:
step 3.3, performing singular value decomposition on the sampling matrix Y by a singular value decomposition technology, wherein the singular value decomposition is decomposed into a matrix lambda of a left singular matrix U, M xL of M x M dimensions and a right singular matrix V of L x L dimensions H Wherein the diagonal of matrix Λ is singular and the remaining elements are 0, namely:
Y＝UΛV H
wherein [ (S)] H Representing the conjugate transpose operation of the matrix.
Step 3.4, according to the sampling matrix and the right singular square matrix V H And M x 1-dimensional column vectors
Obtaining echo data vector after dimension reduction, wherein the echo data vector after dimension reduction is M multiplied by 1 dimension,/->
Zero column vector for L-1 dimension, namely:
Y sv ＝YVT。
and 4, constructing a search airspace dictionary based on an angle search range of the meter wave array radar and an echo model of the multipath signal, and dividing the whole search airspace dictionary into J parts, wherein J is greater than M.
Wherein the search range is initialized. Determining an angular search range [ theta ] of a meter wave array radar start ,θ end ]，θ start Represents the minimum value, theta, of the angular search of the meter wave array radar end The maximum value of angle search of the meter wave array radar is shown, and theta is generally taken end -θ start ≤θ 3dB . Generally set meter wave array radar pointing theta x =0° parallel to the array, the angular search range of the meter-wave array ground radar is generally set to θ start =0° and θ end ＝θ 3dB . Wherein θ 3dB Representing the beam half-power width of the signal that the array radar transmits to its target of detection range,
m represents the total number of antenna array elements included in the meter wave array radar, d is the spacing of the antenna array elements, lambda represents the carrier frequency wavelength of a target transmitting signal of the meter wave array radar to the detection range of the meter wave array radar, and lambda=c/f is provided 0 C represents the speed of light, f 0 Representing the carrier center frequency of the signal transmitted by the meter wave array radar to the target of the detection range.
Step 4.1, obtaining direct wave signal data x received by an mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t)。
Specifically, since the direct echo signal and the multipath echo signal are superimposed in the same distance unit, since the multipath echo signal has a slightly long distance and undergoes primary reflection, a complex coefficient is required to describe the wave path difference between the multipath wave and the direct wave and the loss after ground reflection. Therefore, the direct wave signal data x received by the mth antenna array element dm (t) can be expressed as:
wherein s (t) isTransmitting signals of antenna array element, n m (t) is the additive white noise of the m-th antenna element channel, θ d And d is the interval between array elements for the target pitch angle to be estimated.
Multipath wave signal data x received by mth antenna array element mm (t) can be expressed as:
wherein θ s For the multipath pitch angle of the target, ρ is a reflection coefficient, α=2pi Δr/λ is a phase difference between the direct wave and the multipath wave due to time delay, and Δr is a wave path difference between the direct wave and the multipath wave.
Step 4.2, direct wave signal data x received by the mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t) superposing to obtain composite data x received by the mth antenna array element m (t) and combining the data x m (t) echo model recorded as multipath signal, composite data x m (t) is:
step 4.3, according to the composite data x received by M antenna array elements m (t) obtaining composite data x of M antenna array elements m A sampling matrix X (t) formed by (t), the sampling matrix X (t) being:
wherein the complex variables
Described is the total multipath loss, column vector N (t) = [ N 1 (t),...,n m (t)] T The additive white noise of M array element channels is described, and a (-) represents the corresponding angle of the radarSteering vector under array manifold, a (θ d ) For the steering vector of the pitch angle of the target to be estimated under the radar array manifold, a (θ s ) Is the steering vector of the multipath pitch angle of the target under the radar array manifold.
Step 4.4, obtaining a composite steering vector phi according to the sampling matrix X (t) a (θ j )。
Specifically, the composite data x of M antenna array elements is used m If the current array is a classical plane multipath scene and the height difference hr from the center of the array to the reflecting surface is known, the classical array priori can be obtained according to the geometrical relationship of the radar, the target and the reflecting surface in the classical multipath signal model
Defining atoms of the dictionary as composite steering vectors containing direct waveguide steering vectors and multipath steering vectors of the received signal of the target at corresponding elevation angles, and defining the atoms as:
wherein phi is a To search the airspace dictionary, θ j To search for a pitch angle, a (θ j ) Is the pitch angle theta j Steering vector, Φ, under the radar array manifold a (θ j ) Representative target is represented by a (θ) j ) The steering vector represents a composite steering vector of the received signal when in direction.
Step 4.5, searching for the range [ θ ] based on the angle start ,θ end ]At fixed search intervals
Dispersing the whole airspace into J-shaped grids, wherein the atomic vector of each grid is corresponding phi a (θ j ) Searching the airspace dictionary phi a Matrix expressed as M x J dimensions:
wherein phi is a To search the spatial dictionary, a (θ start ) Searching for a steering vector, a (θ) end ) The steering vector of the maximum under the radar array manifold is searched for the angle of the meter wave array radar.
And 5, performing preliminary estimation on the elevation angle of the target by using an orthogonal matching pursuit algorithm based on the echo data vector after the dimension reduction and the search airspace dictionary to obtain the initial estimated elevation angle of the target and the sparse coefficient vectors of the K corresponding targets.
Step 5.1, selecting the residual error e with the current iteration number k k And adding the dictionary atom with the largest inner product into the current support index set to obtain an updated support index set.
In l 1 Sparse solution under norm condition instead of solving for l 0 And (3) a norm solution, wherein a solution result is constrained in an error-shaped form, so that a solution target elevation problem can be subjected to sparse representation, and the sparse representation is expressed as:
wherein θ k For the estimated elevation angle of the kth target, gamma k Expressed as the kth target corresponds to a (θ k ) Sparse coefficient of direction, and sparse coefficient vector gamma of K targets (1) From gamma k Composition, i.e. gamma (1) ＝[γ 1 ,γ 2 ,...,γ k ] (1) . And initializing the sparse coefficient corresponding to all atoms to be 0.
Definition eta k For the kth iteration [ theta ] start ,θ end ]Sparse vector composed of sparse coefficients of all atoms in the sphere, residual e k Is the error at the kth iteration, i.e. e k ＝Y sv -Φ a η k Initializing residual e 0 ＝Y sv The method comprises the steps of carrying out a first treatment on the surface of the Defining a support index set as a constituent jointReceiving dimension-reducing signal Y sv Initializing a support index set to be an empty set, i.e
The algorithm prior sparsity is K, representing that the received signal Y is formed by K target echoes in total sv 。
Selecting a residual e from the current iteration number k k The atoms with the largest inner products:
wherein lambda is k The dictionary atoms selected for the kth iteration,<·,·>for the two-vector inner product, |·| is the absolute value. Adding the found relevant elements into the current support index set:
Γ k+1 ＝Γ k ∪{λ k }
wherein, U is a union operation, Γ k For the support index set corresponding to the kth iteration, Γ k+1 And (3) supporting the index set corresponding to the k+1st iteration.
Step 5.2, according to the updated support index set Γ k+1 Combined into matrix phi Γk+1 The orthogonal projection operator P of this atomic space is then:
wherein [ (S)] T For transpose operation of matrix, [. Cndot.] -1 Inversion operation for the matrix;
by subtracting from the residual e k Subtracting it from
The orthographic projection on the stretched space obtains updated residual error e k+1 ，e k+1 ＝e k -Pe k ；
Recording the sparse coefficient corresponding to the selected dictionary atom as gamma k ＝Pe k 。
Step 5.3, let k=k+1, at this time, complete one complete iteration is completed, return to step 5.1, until reaching the iteration exit requirement k=k.
And 5.4, obtaining elevation angle estimation corresponding to the K targets according to dictionary atoms in the support index set after iteration, and obtaining sparse coefficient vectors of the K targets of the orthogonal matching pursuit algorithm according to the sparse coefficients.
The elevation angle estimates for the K targets are:
θ (1) ＝[θ 1 ,θ 2 ,θ 3 ,...,θ K ] (1)
wherein the elevation estimate of the kth target
The airspace position corresponding to the kth atom of the supporting index set;
the sparse coefficient vectors of the K targets are:
γ (1) ＝[γ 1 ,γ 2 ,γ 3 ,...,γ K ] (1)
wherein the sparsity coefficient gamma of the kth target k ＝Pe k 。
And 6, updating the estimation of the grid disturbance quantity and the target sparse vector by an alternate iteration method based on the initial estimated elevation angle and the sparse coefficient vector of the target, updating the grid point to the real elevation angle position of the target by the grid disturbance, and further obtaining the elevation angle estimation value of the target.
Specifically, adding grid disturbance delta theta to the sparse reconstruction model to form a new signal estimation model, and jointly estimating the new signal estimation model and a target sparse vector gamma to estimate a result theta in the step 5 (1) And gamma is equal to (1) As an initial value, the estimation of the unknown quantities delta theta and gamma is updated by an alternate iterative method, grid points are updated to the real elevation positions of the targets through grid disturbance, and then the elevation estimation value of the targets is obtained, wherein the elevation estimation value of the targets is a sparse reconstruction elevation estimation result facing to off-grid targets.
Step 6.1, introducing grid disturbance delta theta, and when the sparsity is K, obtaining the grid disturbance delta theta as follows:
δθ＝[δθ 1 ,δθ 2 ,δθ 3 ,...,δθ K ]
wherein δθ k Original grid point theta of nearest dictionary for kth target distance k Is an unknown disturbance of (1).
Step 6.2, obtaining an estimation model according to the grid disturbance delta theta and the target sparse vector gamma
Delta theta is added into the target estimation model and is used as one of estimated variables to carry out joint estimation with the target sparse vector gamma. The new estimation model can therefore be written as:
wherein Y is sv Is the received echo signal; k is a target sequence number, and K is a target number; gamma ray k The sparse coefficient of the kth target represents the strength of the signal; phi a Is a dictionary in which delta theta k Representing the original lattice point theta of the kth target from the nearest dictionary k Unknown disturbance of (2), thus phi a (θ k +δθ k ) Represents the atomic vector that falls on the kth target true position after perturbation. In the constraint, Δ represents the original dictionary interval, i.e., the perturbation is limited to not more than half the original dictionary interval. In order to obtain the estimation of the most compared received signals Y, the disturbance values and the sparse coefficients of the grid points of the original dictionary are estimated in a combined mode, and therefore accurate measurement of off-grid targets is achieved.
Step 6.3, let t=1, where T is the current iteration number, T max For the maximum iteration times of the algorithm, the initial values of the sparse vectors of the K targets are the sparse coefficient vector gamma obtained in the step 5 (1) The initial elevation angle estimation values of the K targets are the initial target estimated elevation angle theta obtained in the step 5 (1) 。
And 6.4, fixing the sparse vectors of the K targets unchanged, and optimizing the grid disturbance quantity based on the estimation model.
Specifically, the sparse vectors of K targets are fixed
Invariable, optimize the disturbance quantity
The optimization objective function is:
the model of the above equation is consistent with the least squares problem, but it is no longer linear. Solving the nonlinear problem would involve a significant amount of computational complexity. Thus, a linear optimization solution is performed on the above equation. For nonlinear part
Using the taylor series expansion to the first term, it can be rewritten as:
thus, the objective function can be rewritten as:
wherein ζ= [ δθ ] 1 ,...,δθ K ]To record the K1 vector of disturbances, [. Cndot.]' is the derivation of the matrix vector. At this time, the objective function is a standard least square problem, and a closed solution exists.
Step 6.5, according to the echo data vector after dimension reduction and the sparse vector gamma of K targets of the t-th iteration (t) Obtaining the data residual error of the t-th iteration by corresponding dictionary atoms
Data residual->
The method comprises the following steps:
step 6.6, solving the bias derivative theta of the variables of each dictionary atom of the K targets of the t-th iteration k Obtaining a partial guide result, and obtaining a partial guide dictionary matrix A according to the partial guide result (t) 。
Specifically, dictionary atoms for K targets according to the t-th iteration
Calculating the respective variable theta of each dictionary atom k The deviation is recorded as->
Obtaining a partial guide dictionary matrix A by calculation according to the obtained partial guide result and the sparse vector of the target (t) ：
Step 6.7, according to the data residual error
Partial guide dictionary matrix A (t) Get new objective function->
Thereby obtaining the grid disturbance quantity of the t-th iteration.
Specifically, the rewritten objective function
For the standard least square problem, a closed solution exists, and the calculated closed solution result is as follows:
since the disturbance of the grid points of the dictionary must be a real value, the dictionary disturbance quantity of the t-th iteration is as follows:
wherein Re {. Cndot. Is a real value of the corresponding vector.
Step 6.8, obtaining updated dictionary lattice point positions according to the grid disturbance quantity of the t-th iteration, namely:
step 6.9, fixing the dictionary lattice point positions of the K targets unchanged, optimizing sparse vectors of the K targets by using an optimization objective function, and obtaining an update matrix B according to the updated dictionary lattice point positions (t+1) 。
Specifically, the dictionary lattice point positions of K targets are fixed
Invariably, optimize sparse vector of K targets +.>
The optimization objective function is:
the above equation is consistent with a model of the least squares solution problem shaped as ax=b. Updating the lattice point theta according to the updated dictionary (t+1) Calculating to obtain an updated matrix B (t+1) Updating the lattice point corresponding dictionary atoms for the dictionary:
step 6.10, based on update matrix B (t+1) Obtaining updated sparse vectors of K targets according to a closed solution of a linear least square solution, namely:
γ (t+1) ＝((B (t+1) ) H B (t+1) ) -1 (B (t+1) ) H Y sv 。
step 6.11, let t=t+1, determine if t=t max If yes, stopping iteration, and at the moment, stopping the iteration of the dictionary lattice point positions
Namely, the elevation angle estimation corresponding to K targets, < >>
If not, returning to step 6.4 until t=t max 。
The invention provides a sparse reconstruction elevation angle estimation method for an off-grid target, which directly solves the off-grid problem in a discrete parameter space, namely, a disturbance item is added to a pre-defined grid, so that the off-grid target is accurately estimated. The method can reduce the elevation angle estimation error of the low-altitude target and improve the angle estimation performance of the radar on the low-altitude target.
The effect of the invention is further illustrated by the following simulation experiments:
1. simulation conditions
Default parameters: the linear array has 16 array elements, the working wavelength is 1m, the distance between the array elements is half of the working wavelength, the height of the radar array center from the reflecting surface is 30m, the target distance is 100km, the multipath reflection coefficient is-0.9, and the multipath wave incident angle is theta s ＝-θ d The sampling snapshot number is 1, and the noise obeys the average valueA complex gaussian random distribution of zero. And independently performing multiple Monte Carlo experiments, and counting Root Mean Square Error (RMSE) of the experimental results according to the following formula so as to measure the quality of angle estimation performance.
Wherein N is the number of independent Monte Carlo experiments, θ d Is the true value of the target elevation angle,
the results of the ith Monte Carlo experiment are shown.
2. Emulation content
Simulation 1: when the real elevation angle of the target is 2.7 degrees, the elevation angle of the target is estimated by using a traditional orthogonal matching pursuit algorithm (OMP) and the method of the invention respectively. Wherein the dictionary of the orthogonal matching pursuit algorithm sets the grid spacing to 0.2 °. 100 Monte Carlo experiments were independently performed to obtain a variation curve of the root mean square error of the angle estimation value with the signal to noise ratio, as shown in FIG. 2.
Simulation 2: the dictionary of the orthogonal matching pursuit algorithm is set to have grid intervals of 0.2 degrees, the echo signal-to-noise ratio is 20dB, the elevation angle of the target is estimated by using the method and the traditional orthogonal matching pursuit algorithm, 100 Monte Carlo experiments are independently carried out, and the result of the 100 Monte Carlo experiments of the estimation result is shown in figure 3.
3. Simulation analysis
As can be seen from fig. 2, when the elevation angle of the target is 2.7 °, the angle estimation error of the present invention for the target is smaller than that of the conventional orthogonal matching pursuit algorithm. The target elevation angle is 2.7 degrees and does not fall on the lattice points of the dictionary, and the lattice point closest to the target elevation angle is theta i =2.6° and θ i =2.8°, and therefore the theoretical accuracy limit of a conventional orthogonal matching pursuit algorithm should be rmse=0.1°. As can be seen from FIG. 2, when the signal-to-noise ratio reaches 20dB, the estimation performance of the conventional orthogonal matching pursuit algorithm reaches the upper limit, the theoretical precision limit caused by the off-grid target can not be broken through any more, and the algorithm breaks through the theoretical precision limit at about 15dBAnd a better estimation performance can be obtained.
As is more evident from fig. 3, the angle measurement result of the OMP algorithm is mostly converged to 2.6 ° and 2.8 ° under the signal-to-noise ratio condition of 20dB, while the Off-Grid algorithm can be converged to around the true target position of 2.7 °.
As can be seen from simulation experiments, for low-altitude targets, the angle estimation performance of the method is obviously superior to that of the traditional orthogonal matching pursuit algorithm, the angle estimation error is reduced, and the capability of detecting off-grid targets is provided for the measurement of elevation angles by using a sparse reconstruction algorithm for the meter wave radar.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the invention.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
Although the present application has been described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the figures, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (8)
1. The sparse reconstruction elevation angle estimation method for the off-grid target is characterized by comprising the following steps of:
step 1, a meter wave array radar transmits signals of M dimensions to a target in a detection range of the meter wave array radar and then receives echo signals from the target;
step 2, carrying out L times of digital sampling snapshot on the echo signals of the target based on the target distance unit to obtain L times of digital sampling snapshot data of M antenna array elements;
step 3, obtaining a sampling matrix according to the first digital sampling snapshot data of the mth antenna array element echo, and processing the sampling matrix through a singular value decomposition technology to obtain an echo data vector after dimension reduction, wherein M is more than 0 and less than or equal to M;
step 4, constructing a search airspace dictionary based on the angle search range of the meter wave array radar and an echo model of the multipath signal, and dividing the whole search airspace dictionary into J parts, wherein J is greater than M;
step 5, based on the echo data vector after dimension reduction and a search airspace dictionary, carrying out preliminary estimation on the elevation angle of the target by utilizing an orthogonal matching pursuit algorithm to obtain initial estimated elevation angles of the target and sparse coefficient vectors of the K corresponding targets;
and 6, updating the estimation of the grid disturbance quantity and the target sparse vector by an alternate iteration method based on the initial estimated elevation angle and the sparse coefficient vector of the target, updating the grid point to the real elevation angle position of the target by the grid disturbance, and further obtaining the elevation angle estimation value of the target.
2. The off-grid target-oriented sparse reconstruction elevation angle estimation method of claim 1, wherein the meter wave array radar comprises M isotropic array elements arranged at half-wavelength intervals placed perpendicular to an array ground plane.
3. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, wherein the step 2 comprises:
step 2.1, determining a target distance unit where the target is located by performing pulse compression processing and moving target detection on the echo signal of the target;
and 2.2, carrying out L times of digital sampling snapshot on the echo signals of the target at the target distance unit to obtain L times of 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, wherein the step 3 comprises:
step 3.1, arranging the L times of digital sampling snapshot data of the echo of the mth antenna array element according to the sequence to obtain a sampling vector of the echo of the mth antenna array element detection target;
step 3.2, obtaining a sampling matrix formed by sampling vectors of M antenna array elements according to the sampling vectors of echoes of the detection targets of the M antenna array elements;
step 3.3, performing singular value decomposition on the sampling matrix by a singular value decomposition technology, wherein the singular value decomposition is decomposed into a matrix lambda of a left singular matrix U, M xL of M x M dimensions and a right singular matrix V of L x L dimensions H Wherein the diagonal of the matrix Λ is a singular value and the rest elements are 0;
step 3.4, according to the sampling matrix and the right singular square matrix V H And M x 1-dimensional column vectors
Obtaining echo data vector after dimension reduction, < + >>
Is a zero column vector of L-1 dimension.
5. The off-grid target-oriented sparse reconstruction elevation angle estimation method of claim 1, wherein the meter wave array radar angle search range is [ theta ] start ,θ end ]，θ start Representing the minimum value, theta, of the angle search of the meter wave array radar end Representing an angle search maximum of the meter wave array radar, wherein θ end -θ start ≤θ 3dB ，θ 3dB And the half-power width of the wave beam of the target transmitting signals of the detection range of the meter wave array radar is represented.
6. The sparse reconstruction elevation angle estimation method for off-grid targets of claim 5, wherein step 4 comprises:
step 4.1, obtaining direct wave signal data x received by an mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t)；
The direct wave signal data x dm (t) is:
wherein s (t) is the transmitting signal of the antenna array element, n m (t) is the additive white noise of the m-th antenna element channel, θ d The pitch angle is a target pitch angle to be estimated;
the multipath wave signal data x mm (t) is:
wherein θ s As the multipath pitch angle of the target, ρ is a reflection coefficient, α=2pi Δr/λ is the phase difference between the direct wave and the multipath wave due to time delay, and Δr is the wave path difference between the direct wave and the multipath wave;
step 4.2, direct wave signal data x received by the mth antenna array element dm (t) and mth antenna array element received multipath wave signal data x mm (t) superposing to obtain composite data x received by the mth antenna array element m (t) and combining the data x m (t) an echo model of the multipath signal;
step 4.3, according to the composite data x received by M antenna array elements m (t) obtaining composite data x of M antenna array elements m A sampling matrix X (t) constituted by (t);
step 4.4, obtaining a composite steering vector phi according to the sampling matrix X (t) a (θ j ) The composite steering vector phi a (θ j ) The method comprises the following steps:
wherein phi is a To search the airspace dictionary, θ j To search for a pitch angle, a (θ j ) Is the pitch angle theta j Steering vector, Φ, under the radar array manifold a (θ j ) Representative target is represented by a (θ) j ) The steering vector represents the composite steering vector of the received signal, hr is the height difference from the center of the array to the reflecting surface;
step 4.5, searching for the range [ θ ] based on the angle start ,θ end ]At fixed search intervals
Dispersing the whole airspace into J-shaped grids, wherein the atomic vector of each grid is corresponding phi a (θ j ) Searching the airspace dictionary phi a Matrix expressed as M x J dimensions:
wherein, the liquid crystal display device comprises a liquid crystal display device,Φ a to search the spatial dictionary, a (θ start ) Searching for a steering vector, a (θ) end ) The steering vector of the maximum under the radar array manifold is searched for the angle of the meter wave array radar.
7. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, wherein the step 5 comprises:
step 5.1, selecting the residual error e with the current iteration number k k Adding the dictionary atom with the largest inner product into the current support index set to obtain an updated support index set, wherein the dictionary atom is as follows:
wherein lambda is k The dictionary atoms selected for the kth iteration,<·,·>for the inner product of two vectors, |·| is the absolute value;
step 5.2, combining the support index sets into a matrix according to the updated support index sets
The orthogonal projection operator P of this atomic space is then:
wherein [ (S)] T For transpose operation of matrix, [. Cndot.] -1 Inversion operation for the matrix;
by subtracting from the residual e k Subtracting it from
The orthographic projection on the stretched space obtains updated residual error e k+1 ，e k+1 ＝e k -Pe k ；
The selected dictionary atom corresponds to a sparse coefficient of gamma k ＝Pe k ；
Step 5.3, let k=k+1, finish a complete iteration at this moment, return to step 5.1, until reaching the iteration and withdrawing the requirement k=k;
and 5.4, obtaining elevation angle estimation corresponding to the K targets according to dictionary atoms in the support index set after iteration, and obtaining sparse coefficient vectors of the K targets of the orthogonal matching pursuit algorithm according to the sparse coefficients.
8. The sparse reconstruction elevation angle estimation method for off-grid targets according to claim 1, wherein the step 6 comprises:
step 6.1, introducing grid disturbance delta theta, and when the sparsity is K, obtaining the grid disturbance delta theta as follows:
δθ＝[δθ 1 ,δθ 2 ,δθ 3 ,...,δθ K ]
wherein δθ k Original grid point theta of nearest dictionary for kth target distance k Unknown disturbance of (a);
step 6.2, obtaining an estimation model according to the grid disturbance delta theta and the target sparse vector gamma;
step 6.3, let t=1, where T is the current iteration number, T max For the maximum iteration times of the algorithm, the initial values of the sparse vectors of the K targets are the sparse coefficient vector gamma obtained in the step 5 (1) The initial elevation angle estimation values of the K targets are the initial target estimated elevation angle theta obtained in the step 5 (1) ；
Step 6.4, fixing the sparse vectors of the K targets unchanged, and optimizing grid disturbance quantity based on an estimation model;
step 6.5, according to the echo data vector after dimension reduction and the sparse vector gamma of K targets of the t-th iteration (t) Obtaining the data residual error of the t-th iteration by corresponding dictionary atoms
Step 6.6, K mesh for the t-th iterationEach dictionary atom of the target deflects its variable by θ k Obtaining a partial guide result, and obtaining a partial guide dictionary matrix A according to the partial guide result and the sparse vector of the target (t) ；
Step 6.7, according to the data residual error
Partial guide dictionary matrix A (t) Get new objective function->
Thereby obtaining the grid disturbance quantity of the t-th iteration;
step 6.8, obtaining updated dictionary lattice point positions according to the grid disturbance quantity of the t-th iteration;
step 6.9, fixing the dictionary lattice point positions of the K targets unchanged, optimizing sparse vectors of the K targets by using an optimization objective function, and obtaining an update matrix B according to the updated dictionary lattice point positions (t+1) ；
Step 6.10, based on update matrix B (t+1) Obtaining updated sparse vectors of K targets according to a closed solution of the linear least square solution;
step 6.11, let t=t+1, determine if t=t max If yes, stopping iteration, wherein the dictionary lattice point positions are elevation angle estimates corresponding to K targets, otherwise, returning to step 6.4 until t=T max 。
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