CN115825944A - Single-snapshot multi-target incoming wave direction estimation method based on external radiation source radar - Google Patents
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Abstract
The invention discloses a single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar, which comprises the following steps of: receiving an echo signal of a target and a direct wave signal of an external radiation source by using an array antenna of an external radiation source radar, performing distance-Doppler two-dimensional mutual fuzzy calculation, and constructing an observation vector; constructing a grid point selection set, generating a target reference dictionary matrix by using the grid point selection set, and constructing a representation dictionary matrix by using the target reference dictionary matrix and the offset estimation matrix; constructing and solving a non-convex substitution sparse solution model to obtain a solution vector of the non-convex substitution sparse solution model; and constructing a rationality judgment function, calculating a rationality judgment function value of a solution vector of the non-convex substitution sparse solving model, carrying out grid rationality judgment, and obtaining an estimated value of an incoming wave direction of each target according to a judgment result. The method and the device realize multi-target incoming wave direction estimation under single snapshot, have the advantages of simplicity and high efficiency, and improve the accuracy and precision of estimation.
Description
Technical Field
The invention belongs to the technical field of electronics, and particularly relates to a single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar.
Background
Currently, in radar, sonar and wireless communication systems, the estimation problem of the direction of arrival (DOA) of an array signal has been a research focus in the field of signal processing and has wide application, and currently, high-resolution adaptive DOA estimation methods mainly include MVDR (minimum variance discrete response), MUSIC (multiple signal classification), covariance matching method, and the like. However, due to the influence of high-speed motion and multipath propagation of the target or the facing of a burst target, the obtained snapshot data are very limited, and inaccurate estimation of the spatial covariance matrix is caused, so that the estimation accuracy of methods such as MVDR and MUSIC is greatly reduced, and therefore, the method has important significance for exploration and research of a DOA estimation method of single snapshot data.
With the development of Compressed sensing (Compressed sensing) technology, research on sparse signal recovery-based DOA estimation has been greatly developed, in recent years, sparse recovery algorithms such as OMP (Orthogonal Matching Pursuit) and l1 norm minimization have been applied to research on such problems, and although these works provide reasonable bases for their algorithms, these algorithms have strict applicable conditions, and not only their measurement matrices need to satisfy RIP conditions, but also their RIC constants (verified Isometry constants) need to satisfy some properties, however, it is difficult to verify RIP conditions of given matrices themselves as an NP-HARD problem, and the current RIP estimation conclusion is only applicable to random matrices, but in practical application, DOA measurement matrices acquired by using actual target acquisition data hardly satisfy such random structures, and thus it is difficult to directly verify RIP conditions, so that the practicability of model theory in practical scenarios is difficult to be fully guaranteed.
Disclosure of Invention
The invention aims to: the invention provides a single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar, which can effectively realize the estimation of multi-target incoming wave directions according to single-snapshot data of a receiving array and improve the target multi-target positioning capability of a system.
The invention discloses a single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar, which comprises the following steps of:
s1, receiving an echo signal of a target and a direct wave signal of an external radiation source by using an array antenna of an external radiation source radar, performing distance-Doppler two-dimensional mutual fuzzy calculation on the received echo signal and the received direct wave signal to obtain a mutual fuzzy calculation result, and constructing an observation vector aiming at a distance-Doppler unit corresponding to the target and a corresponding mutual fuzzy calculation result;
s2, dividing an angle estimation range of the target into a plurality of regions, selecting grid points in each region, constructing a grid point selection set, generating a target reference dictionary matrix by using the grid point selection set, generating an offset estimation matrix according to the target reference dictionary matrix, and constructing a representation dictionary matrix by using the target reference dictionary matrix and the offset estimation matrix;
s3, constructing a non-convex substitution sparse solution model according to the observation vector and the expression dictionary matrix, and solving the non-convex substitution sparse solution model by using an immobile point iterative algorithm according to a non-convex substitution function to obtain a solution vector of the non-convex substitution sparse solution model; the first half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amount of the selected grid points in each region, and the second half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amount of the selected grid points in each region;
and S4, constructing a rationality judgment function, calculating a rationality judgment function value of a solution vector of the non-convex substitution sparse solving model, carrying out grid rationality judgment, and obtaining an estimated value of an incoming wave direction of each target according to a judgment result.
The step S1 specifically includes: receiving an echo signal of a target by using a first array antenna of an external radiation source radar, enabling a receiving beam of a second array antenna of the external radiation source radar to point to an external radiation source, enabling the receiving beam to receive a radiation signal of the external radiation source, and taking the radiation signal as a direct wave signal;
obtaining a discrete variable dr (N) after discrete sampling is carried out on the direct wave signal, wherein N =1, 2. The first array antenna of the external radiation source radar comprises M paths of antennas, the distance between the antennas is equal to the half wavelength of the direct wave signal, and the discrete expression of the echo signal of the target received by the mth path antenna of the first array antenna is as follows:
wherein ,Nc To a target amount, θ i The direction of arrival of the echo signal of the ith target, a i,m The amplitude, tau, of the echo signal of the ith target received by the mth antenna of the first array antenna i and fi Time delay and frequency delay of echo signal of ith target relative to direct wave, A m (θ i ) Is the utilization angle theta of the mth antenna i And generating a guide vector element, wherein the expression of the guide vector element is as follows:
wherein d is the antenna spacing of the first array antenna of the external radiation source radar, λ is the wavelength of the direct wave signal, and M is the number of antennas;
the distance-Doppler two-dimensional mutual fuzzy calculation is carried out on the echo signals received by the array antennas and the direct wave signals, then the mutual fuzzy calculation result of the echo signals received by each path of antenna of the first array antenna is expressed as,
wherein ,Φm (τ, f) is the mutual fuzzy calculation result of the echo signal received by the mth antenna of the first array antenna under the time delay τ and the frequency delay f, dr * (n- τ) represents the conjugate transpose of the discrete variable dr (n) with time delay τ;
when N is present c The time delay and the frequency delay of each target are located in the same range-Doppler unit (tau) * ,f * ) Then, the mutual ambiguity calculation result corresponding to the range-Doppler unit is expressed as,
wherein ,Bi (τ * ,f * ) Complex envelope in range-doppler cell (τ) representing echo signal corresponding to ith target * ,f * ) Value of w m (τ * ,f * ) Indicating that the echo signal received by the m-th antenna is in the range-Doppler cell (tau) * ,f * ) The mutual fuzzy calculation results of the echo signals received by the first array antenna are arranged according to the antenna position sequence of the first array antenna to obtain an observation vector b, and the expression of the observation vector b is as follows:
b＝[Φ 1 (τ * ,f * ),Φ 2 (τ * ,f * )，...，Φ M (τ * ,f * )]，
thereby obtaining an observation vector.
The step S2 specifically includes:
s21, determining an angle estimation range [ theta ] according to the direction range of the target min ,θ max ]Uniformly dividing the angle estimation range of the target into G areas, randomly selecting a grid point in the area with the smallest angle value according to the sequence of small and large angle values in the areas, then randomly selecting a grid point alpha in the next area, and generating a grid point selection set gamma by using all the selected grid points;
s22, generating a reference dictionary matrix F by utilizing a grid point selection set gamma, wherein F belongs to C M×|Γ| ，C M×|Γ| A complex matrix set representing M rows | Γ | columns, | Γ | is the number of elements in the set Γ, and the expression of the column vector for F is:
F i ＝[A 1 (α i ),A 2 (α i )...,A M (α i )] T ，
wherein ,Fi The ith column vector, α, representing the matrix F i E Γ, the coherence μ (F) of the matrix F is calculated by the formula:
s23, judging whether the coherence of the generated reference dictionary matrix is larger than or equal to a judgment threshold epsilon, if so, removing the grid points alpha from the grid point selection set gamma, reselecting the grid points from the region where the grid points alpha are located, generating a grid point selection set again, and returning to the step S22; if the selection times of the grid points reach the upper limit, the step S24 is carried out; if the coherence of the generated reference dictionary matrix is less than the judgment threshold epsilon, entering step S25;
s24, selecting a middle point of a region where the value of the currently selected grid point is located in the middle of the region as a new grid point, adding the new grid point as a finally selected grid point in the region into a grid point selection set, randomly selecting grid points in the next region according to the sequence of small and large internal angular values of the region, adding the grid points into the grid point selection set, and entering step S22, or entering step S26 if the selection of the grid points of all the regions is finished;
s25, reserving the current grid point in the grid point selection set gamma, entering the next area to select the grid point according to the sequence of small and large internal angle values in the area, generating a grid point selection set again, entering step S22, recording the final grid point selection set if the grid points of all the areas are selected, recording the final grid point selection set as a first grid point selection set, and entering step S26;
s26, after the grid points of all the areas are selected, generating a target reference dictionary matrix FZ according to the first grid point selection set, wherein the expressions of the ith row and the jth column elements of the target reference dictionary matrix FZ are as follows:
FZ i,j ＝A i (α j ),
and obtaining an offset estimation matrix H by using the generated target reference dictionary matrix FZ, wherein H belongs to C M×|Γ| The expression of the ith row and jth column element of the offset estimation matrix H is,
wherein ,Ai ' (. Alpha.) is represented by A i ' (α) derivation of α;
constructing a dictionary expression matrix omega by using the target reference dictionary matrix FZ and the offset estimation matrix H, wherein the expression dictionary matrix omega belongs to C M×2|Γ| The expression representing the dictionary matrix is Ω = [ FZ, H]Thereby obtaining a representation dictionary matrix.
The step S3 specifically includes:
designing a non-convex substitution function f p (x) The expression is
Wherein x is an independent variable, e is a natural constant, p is a parameter of a non-convex substitution function, and a corresponding pseudo-norm is defined for the vector x
The expression is as follows:
x i for the ith element in the vector x, a non-convex substitution sparse solution model is constructed according to the observation vector and the representation dictionary matrix, wherein the expression is as follows,
thereby constructing and obtaining a non-convex substitution sparse solution model.
The solving of the non-convex substitution sparse solution model by using the fixed point iterative algorithm specifically comprises the following steps:
s31, randomly generating an initial variable as a current variable;
s32, taking the current variable as input, and substituting the current variable into an optimal solution fixed point expression P (x) to obtain a middle matrix psi, namely psi = P (x), wherein the middle matrix psi is a diagonal matrix, and elements P (x) of the ith row and the ith column of the diagonal matrix i,i Is P (x) i,i ＝|x i |/f′ p (x i), wherein ,xi The i-th element, f 'of an input variable x representing P (x)' p (x i ) Representing a function f for non-convex substitution p () Derivation is carried out; obtaining the current variable x by using the intermediate matrix psi k The calculation formula of the one-time iteration updating value is as follows:
completing one iteration of the current variable;
s33, judging whether the difference value between the current variable and the primary iteration updating value of the current variable is smaller than a convergence threshold value or reaches a set iteration frequency, if the two conditions are not met, taking the primary iteration updating value of the current variable as input, returning to the step S32, and if the two conditions are met, utilizing the variable x obtained by the last iteration updating z The support set S is constructed such that,
represents the variable x z The support set is used as the constraint of a least square model, and a final solution vector is obtained by using the least square model, wherein the calculation process is as follows:
the final solution x at this time * Namely, the solution vector of the non-convex substitution sparse solution model is obtained.
The step S4 specifically includes:
s41, constructing a rationality judgment function g (x), wherein the expression of the rationality judgment function g (x) is as follows:
wherein x is an input vector of the rationality judgment function, and is divided averagely according to the dimension, and x = [ y, z =] T Y is a column vector formed by the first half elements of x, and z is a column vector formed by the second half elements of x;
s42, assuming the resulting first grid point selection set Γ = [ α ] 1 ,α 2 ,.....α G ]G is the number of uniformly divided regions of the angle estimation range, N is the number of elements contained in y, and y is i Is the ith element in y, z i Is the i-th element in z, Δ α i Selecting a minimum spacing, Δ α, for the ith grid point in the set for the first grid point i ＝min(||α i -α i+1 || 2 ,||α i -α i-1 || 2 ) Calculating the final solution x * If the value is less than or equal to the function threshold value
Step S45 is entered; if the final solution x * Is greater than a function threshold
Step S43 is entered;
s43, solving x finally * Dividing the obtained object into x * ＝[y * ,z * ] T ，y * Is x * The column vector z formed by the first half elements of * Is x * The column vector formed by the latter half elements of (a) at y * Selecting the value with the maximum rationality|y i log(y i ) Element y of | i According to the element y i Finding the grid point α in the first grid point selection set Γ corresponding to the serial number, constructing an alternative set based on the grid point, wherein the expression of the constructed alternative set is as follows:
Λ(α*)＝{α|α＝α±k -1 Δα*,k＝1,2,3，4}，
after the candidate set is constructed, replacing the grid points alpha with the grid points in the candidate set Lambda (alpha) one by one, sequentially reconstructing a dictionary expression matrix omega and repeating the step S3 to obtain solution vectors and corresponding rationality judgment function values of the non-convex substitution sparse solving model corresponding to each grid point in the candidate set Lambda (alpha), and judging whether the minimum rationality judgment function value is larger than a function threshold value or not
If it is greater than the function threshold
Step S44 is entered, if the function threshold value is less than or equal to the function threshold value, step S45 is entered;
s44, selecting the grid point with the minimum rationality judgment function value in the alternative set, replacing the grid point alpha, updating the first grid point selection set gamma, reconstructing the expression dictionary matrix omega, repeating the step S3, and solving the final x * Updating, and entering step S43;
s45, utilizing the final solution x * And a first grid point selection set gamma, wherein the estimated value of the wave coming direction of the echo signal of the ith target is obtained by calculation:
θ i ＝α i +z i ,i∈Π，
wherein ,
thereby completing the estimation of the incoming wave direction of the target.
The invention has the beneficial effects that:
based on the sparse recovery-based single snapshot DOA estimation method provided by the invention, firstly, the characteristics of array antenna snapshot data are analyzed, and a sparse recovery model is constructed; and then, obtaining an optimized solution of the sparse recovery model by using a fractional substitution function minimization algorithm, and obtaining corresponding direction information according to the corresponding relation between the solution and the grid point set elements of the measurement matrix, thereby realizing multi-target incoming wave direction estimation under single snapshot. The problem of low accuracy when other algorithms (such as greedy algorithm and l1 norm minimization algorithm) are adopted is avoided, so that the overall algorithm is simpler and more efficient, and the estimation accuracy and precision are improved.
Drawings
FIG. 1 is a flow chart of a multi-target incoming wave direction estimation implementation of an external radiation source radar provided by the present invention;
FIG. 2 is a non-convex substitution function image under different input parameters;
FIG. 3 shows a simulation result of multi-target incoming wave direction estimation;
FIG. 4 is a comparison graph of the effect of the estimation method under different target numbers.
Detailed Description
For a better understanding of the present disclosure, an example is given here.
FIG. 1 is a flow chart of a multi-target incoming wave direction estimation implementation of an external radiation source radar provided by the present invention; FIG. 2 is a non-convex substitution function image under different input parameters; FIG. 3 shows a simulation result of multi-target incoming wave direction estimation; FIG. 4 is a comparison graph of the effect of the estimation method under different target numbers.
The invention discloses a single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar, which comprises the following steps of:
s1, receiving an echo signal of a target and a direct wave signal of an external radiation source by using an array antenna of an external radiation source radar, performing distance-Doppler two-dimensional mutual fuzzy calculation on the received echo signal and the received direct wave signal to obtain a mutual fuzzy calculation result, and constructing an observation vector aiming at a distance-Doppler unit corresponding to the target and a corresponding mutual fuzzy operation result;
the step S1 specifically includes: and receiving the echo signal of the target by using the first array antenna of the external radiation source radar, directing a receiving beam of the second array antenna of the external radiation source radar to the external radiation source, receiving the radiation signal of the external radiation source by using the receiving beam as a direct wave signal.
The satellite signals are used as external radiation source signals, a receiving end of an external radiation source radar respectively receives direct wave signals and target echo signals, and the satellite signals received by the external radiation source radar system are continuous waves. The satellite signal is a digital television broadcast signal. Discrete sampling is performed on the direct wave signal to obtain a discrete variable dr (N), wherein N =1, 2. The first array antenna of the external radiation source radar comprises M paths of antennas, the distance between the antennas is equal to the half wavelength of the direct wave signal, and the discrete expression of the echo signal of the target received by the mth path antenna of the first array antenna is as follows:
wherein ,Nc To a target amount, theta i The direction of arrival of the echo signal of the ith target, a i,m Amplitude of echo signal of ith target, τ i and fi Time delay and frequency delay of echo signal of ith target relative to direct wave, A m (θ i ) Is the utilization angle theta of the mth antenna i And generating a guide vector element, wherein the expression of the guide vector element is as follows:
where d is the antenna spacing of the first array of antennas of the radar of the external radiation source, λ is the wavelength of the direct wave signal, and M is the number of antennas.
The distance-Doppler two-dimensional mutual fuzzy calculation is carried out on the echo signals and the direct wave signals received by the array antennas so as to improve the signal-to-noise ratio of the target and improve the accuracy rate of target detection, then the mutual fuzzy calculation result of the echo signals received by each antenna of the first array antenna is expressed as,
wherein ,Φm (τ, f) is the mutual fuzzy calculation result of the echo signal received by the mth antenna of the first array antenna under the time delay τ and the frequency delay f, dr * (n- τ) represents the conjugate transpose of the discrete variable dr (n) with time delay τ;
for N c If the time delay and the frequency delay of the echo signals of the targets are different, the different targets can be separated through the distance-Doppler units where the respective time delay and the frequency delay are located. When N is present c The time delay and the frequency delay of each target are located in the same range-Doppler unit (tau) * ,f * ) And in the process, the separation of different targets is realized by calculating the mutual fuzzy function corresponding to the distance-Doppler unit.
When N is present c The time delay and the frequency delay of each target are located in the same range-Doppler unit (tau) * ,f * ) Then, the mutual ambiguity calculation result corresponding to the range-Doppler unit is expressed as,
wherein ,Bi (τ * ,f * ) Complex envelope in range-doppler cell (τ) representing echo signal corresponding to ith target * ,f * ) Value of w m (τ * ,f * ) Indicating that the echo signal received by the m-th antenna is in the range-Doppler cell (tau) * ,f * ) The mutual fuzzy calculation results of the echo signals received by the first array antenna are arranged according to the antenna position sequence of the first array antenna to obtain an observation vector b, and the expression of the observation vector b is as follows:
b＝[Φ 1 (τ * ,f * ),Φ 2 (τ * ,f * )，...，Φ M (τ * ,f * )]，
s2, dividing an angle estimation range of the target into a plurality of areas, selecting grid points in each area, constructing a grid point selection set, generating a target reference dictionary matrix by using the grid point selection set, generating an offset estimation matrix according to the target reference dictionary matrix, and constructing a representation dictionary matrix by using the target reference dictionary matrix and the offset estimation matrix;
the step S2 specifically includes:
s21, determining an angle estimation range [ theta ] according to the direction range of the target min ,θ max ]Uniformly dividing the angle estimation range of the target into G areas, randomly selecting a grid point in the area with the smallest angle value according to the sequence of small and large angle values in the areas, then randomly selecting a grid point alpha in the next area, and generating a grid point selection set gamma by using all the selected grid points;
s22, generating a reference dictionary matrix F by utilizing a grid point selection set gamma, wherein F belongs to C M×|Γ| ，C M×|Γ| A complex matrix set representing M rows | Γ | columns, | Γ | is the number of elements in the set Γ, and the expression of the column vector for F is:
F i ＝[A 1 (α i ),A 2 (α i )...,A M (α i )] T ，
wherein ,Fi The ith column vector, α, representing the matrix F i E Γ, the coherence μ (F) of the matrix F is calculated by the formula:
s23, judging whether the coherence of the generated reference dictionary matrix is larger than or equal to a judgment threshold epsilon, if so, rejecting the grid points alpha from the grid point selection set gamma, reselecting the grid points from the area where the grid points alpha are located, generating a grid point selection set again, and returning to the step S22; if the selection times of the grid points reach the upper limit, the step S24 is carried out; if the coherence of the generated reference dictionary matrix is less than the judgment threshold epsilon, entering step S25;
s24, selecting a middle point of a region where the value of the currently selected grid point is located in the middle of the region as a new grid point, adding the new grid point as a finally selected grid point in the region into a grid point selection set, randomly selecting the grid point in the next region according to the sequence of small and large internal angle values in the region, adding the grid point into the grid point selection set, and entering step S22, or entering step S26 if the selection of the grid points of all the regions is finished;
s25, reserving the current grid point in the grid point selection set gamma, entering the next area to select the grid point according to the sequence of small and large internal angle values in the area, generating a grid point selection set again, entering step S22, recording the final grid point selection set if the grid points of all the areas are selected, recording the final grid point selection set as a first grid point selection set, and entering step S26;
s26, after the grid points of all the areas are selected, generating a target reference dictionary matrix FZ according to the first grid point selection set, wherein the expressions of the ith row and the jth column elements of the target reference dictionary matrix FZ are as follows:
FZ i,j ＝A i (α j ),
and obtaining an offset estimation matrix H by using the generated target reference dictionary matrix FZ, wherein H belongs to C M×|Γ| The expression of the ith row and jth column element of the offset estimation matrix H is,
wherein ,Ai ' (. Alpha.) is represented by A i ' (α) is derived from α.
Constructing a dictionary expression matrix omega by using the target reference dictionary matrix FZ and the offset estimation matrix H, wherein the expression dictionary matrix omega belongs to C M×2|Γ| The expression representing the dictionary matrix is Ω = [ FZ, H]；
S3, constructing a non-convex substitution sparse solution model according to the observation vector b and the expression dictionary matrix omega, and solving the non-convex substitution sparse solution model by using a fixed point iterative algorithm according to a non-convex substitution function to obtain a solution vector of the non-convex substitution sparse solution model; the first half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amounts of the grid points selected in each region, and the second half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amounts of the grid points selected in each region.
The step S3 specifically includes:
designing a non-convex substitution function f p (x) The expression is
Wherein x is an independent variable, e is a natural constant, p is a parameter of a non-convex substitution function, and a corresponding pseudo-norm is defined for the vector x
The expression is as follows:
x i for the ith element in the vector x, a non-convex substitution sparse solution model is constructed according to the observation vector and the representation dictionary matrix, wherein the expression is as follows,
the solving of the non-convex substitution sparse solution model by using the fixed point iterative algorithm specifically comprises the following steps:
s31, randomly generating an initial variable as a current variable;
s32, converting the current variable x k As input, the optimal solution stationary point expression P (x) is substituted to obtain a middle matrix Ψ, i.e., Ψ = P (x), where the middle matrix Ψ is a diagonal matrix, and the element P (x) of the ith row and ith column is obtained i,i Is P (x) i,i ＝|x i |/f′ p (x i), wherein ,xi The i-th element, f 'of an input variable x representing P (x)' p (x i ) Representing a function f for non-convex substitution p () Derivation is carried out; obtaining the current variable x by using the intermediate matrix psi k The calculation formula of the one-time iteration updating value is as follows:
completing one iteration of the current variable;
s33, judging whether the difference value between the current variable and the primary iteration updating value of the current variable is smaller than a convergence threshold value or reaches a set iteration frequency, if the two conditions are not met, taking the primary iteration updating value of the current variable as input, returning to the step S32, and if the two conditions are met, utilizing the variable x obtained by the last iteration updating z A support set S is constructed in such a way that,
represents the variable x z The support set is used as the constraint of a least square model, and a final solution vector is obtained by using the least square model, wherein the calculation process is as follows:
the final solution x at this time * Namely, the solution vector of the non-convex substitution sparse solution model.
S4, constructing a rationality judgment function, calculating a rationality judgment function value of a solution vector of the non-convex substitution sparse solving model, carrying out grid rationality judgment, and obtaining an estimated value of an incoming wave direction of each target according to a judgment result;
the step S4 specifically includes:
s41, constructing a rationality judgment function g (x), wherein the expression of the rationality judgment function g (x) is as follows:
wherein x is an input vector of the rationality judgment function, and is divided averagely according to the dimension, and x = [ y, z =] T Y is a column vector formed by the first half elements of x, and z is a column vector formed by the second half elements of x;
s42, assuming the resulting first grid point selection set Γ = [ α ] 1 ,α 2 ,.....α G ]G is the number of uniformly divided regions of the angle estimation range, N is the number of elements contained in y, and y is i Is the ith element in y, z i Is the i-th element in z, Δ α i Selecting a minimum spacing, Δ α, for the ith grid point in the set for the first grid point i ＝min(||α i -α i+1 || 2 ,||α i -α i-1 || 2 ) Calculating the final solution x * If the value is less than or equal to the function threshold value
Step S45 is entered; if the final solution x * Is greater than a function threshold
Step S43 is entered;
s43, solving x finally * Dividing the obtained object into x * ＝[y * ,z * ] T ，y * Is x * The column vector z formed by the first half elements of * Is x * The column vector formed by the latter half elements of (a) at y * Selecting the value | y with the maximum rationality i log(y i ) Element y of | i According to the element y i Finding the grid point α in the first grid point selection set Γ corresponding to the serial number, constructing an alternative set based on the grid point, wherein the expression of the constructed alternative set is as follows:
Λ(α*)＝{α|α＝α±k -1 Δα*,k＝1,2,3，4}，
after the candidate set is constructed, replacing the grid points alpha with the grid points in the candidate set Lambda (alpha) one by one, sequentially reconstructing a dictionary matrix omega and repeating the step S3 to obtain a solution vector and a corresponding rationality judgment function value of a non-convex substitution sparse solving model corresponding to each grid point in the candidate set Lambda (alpha), judging whether the minimum rationality judgment function value is larger than a function threshold value or not, if so, entering the step S44, and if not, entering the step S45;
s44, selecting the grid point with the minimum rationality judgment function value in the alternative set, replacing the grid point alpha, updating the first grid point selection set gamma, reconstructing the expression dictionary matrix omega, repeating the step S3, and solving the final x * Updating, and entering step S43;
s45, utilizing the final solution x * And a first grid point selection set gamma, calculating to obtain an estimated value of the direction of the incoming wave of the ith target,
θ i ＝α i +z i ,i∈Π，
wherein ,
the incoming wave direction of the target is the direction of the echo signal of the target. For an object that does not satisfy i ∈ Π, the object is considered to be absent.
The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (6)
1. A single-snapshot multi-target incoming wave direction estimation method based on an external radiation source radar is characterized by comprising the following steps:
s1, receiving an echo signal of a target and a direct wave signal of an external radiation source by using an array antenna of an external radiation source radar, performing distance-Doppler two-dimensional mutual fuzzy calculation on the received echo signal and the received direct wave signal to obtain a mutual fuzzy calculation result, and constructing an observation vector aiming at a distance-Doppler unit corresponding to the target and a corresponding mutual fuzzy calculation result;
s2, dividing an angle estimation range of the target into a plurality of regions, selecting grid points in each region, constructing a grid point selection set, generating a target reference dictionary matrix by using the grid point selection set, generating an offset estimation matrix according to the target reference dictionary matrix, and constructing a representation dictionary matrix by using the target reference dictionary matrix and the offset estimation matrix;
s3, constructing a non-convex substitution sparse solution model according to the observation vector and the expression dictionary matrix, and solving the non-convex substitution sparse solution model by using a fixed point iterative algorithm according to a non-convex substitution function to obtain a solution vector of the non-convex substitution sparse solution model; the first half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amount of the selected grid points in each region, and the second half elements of the solution vector of the non-convex substitution sparse solution model correspond to the correction amount of the selected grid points in each region;
and S4, constructing a rationality judgment function, calculating a rationality judgment function value of a solution vector of the non-convex substitution sparse solving model, carrying out grid rationality judgment, and obtaining an estimated value of an incoming wave direction of each target according to a judgment result.
2. The method as claimed in claim 1, wherein the method for estimating the incoming wave direction of the single-beat multi-target based on the external radiation source radar,
the step S1 specifically includes: receiving an echo signal of a target by using a first array antenna of an external radiation source radar, enabling a receiving beam of a second array antenna of the external radiation source radar to point to an external radiation source, enabling the receiving beam to receive a radiation signal of the external radiation source, and taking the radiation signal as a direct wave signal;
obtaining a discrete variable dr (N) after discrete sampling is carried out on the direct wave signal, wherein N =1, 2. The first array antenna of the external radiation source radar comprises M paths of antennas, and the distance between the antennas is equal to the half wavelength of the direct wave signal, so that the discrete expression of the echo signal of the target received by the mth path antenna of the first array antenna is as follows:
wherein ,Nc To a target amount, theta i The direction of arrival of the echo signal of the ith target, a i,m The amplitude, tau, of the echo signal of the ith target received by the mth antenna of the first array antenna i and fi Time delay and frequency delay of echo signal of ith target relative to direct wave, A m (θ i ) Is the utilization angle theta of the mth antenna i And generating a guide vector element, wherein the expression of the guide vector element is as follows:
wherein d is the antenna spacing of the first array antenna of the external radiation source radar, λ is the wavelength of the direct wave signal, and M is the number of antennas;
the distance-Doppler two-dimensional mutual fuzzy calculation is carried out on the echo signals received by the array antennas and the direct wave signals, then the mutual fuzzy calculation result of the echo signals received by each path of antenna of the first array antenna is expressed as,
wherein ,Φm (τ, f) is the mutual fuzzy calculation result of the echo signal received by the mth antenna of the first array antenna under the time delay τ and the frequency delay f, dr * (n- τ) represents the conjugate transpose of the discrete variable dr (n) with time delay τ;
when N is present c The time delay and the frequency delay of each target are located in the same range-Doppler unit (tau) * ，f * ) Then, the mutual ambiguity calculation result corresponding to the range-doppler cell is expressed as,
wherein ,Bi (τ * ，f * ) A complex envelope representing the echo signal corresponding to the ith target in a range-Doppler unit (tau) * ，f * ) Value of w m (τ * ，f * ) Indicates that the echo signal received by the mth antenna is in the range-Doppler unit (tau) * ，f * ) The mutual ambiguity calculation results of the echo signals received by the first array antenna are arranged according to the antenna position sequence of the first array antenna to obtain an observation vector b, and the expression of the observation vector b is as follows:
b[Φ 1 (τ * ，f * )，Φ 2 (τ * ，f * )，…，Φ M (τ * ，f * )]，
thereby obtaining an observation vector.
3. The method for single-snapshot multi-target incoming wave direction estimation based on an external radiation source radar as claimed in claim 2,
the step S2 specifically includes:
s21, determining an angle estimation range [ theta ] according to the direction range of the target min ，θ max ]Uniformly dividing the angle estimation range of the target into G areas, randomly selecting a grid point in the area with the smallest angle value according to the sequence of small and large angle values in the areas, then randomly selecting a grid point alpha in the next area, and generating a grid point selection set gamma by using all the selected grid points;
s22, generating a reference dictionary matrix F by utilizing a grid point selection set gamma, wherein F belongs to C M×|Γ| ，C M×|Γ| A complex matrix set representing M rows | Γ | columns, | Γ | is the number of elements in the set Γ, and the expression of the column vector for F is:
F i ＝[A 1 (α i )，A 2 (α i )…，A M (α i )] T ，
wherein ,Fi The ith column vector, α, representing the matrix F i E Γ, the coherence μ (F) of the matrix F is calculated by the formula:
s23, judging whether the coherence of the generated reference dictionary matrix is larger than or equal to a judgment threshold epsilon, if so, removing the grid points alpha from the grid point selection set gamma, reselecting the grid points from the region where the grid points alpha are located, generating a grid point selection set again, and returning to the step S22; if the selection times of the grid points reach the upper limit, the step S24 is carried out; if the coherence of the generated reference dictionary matrix is less than the judgment threshold epsilon, entering step S25;
s24, selecting a middle point of a region where the value of the currently selected grid point is located in the middle of the region as a new grid point, adding the new grid point as a finally selected grid point in the region into a grid point selection set, randomly selecting grid points in the next region according to the sequence of small and large internal angular values of the region, adding the grid points into the grid point selection set, and entering step S22, or entering step S26 if the selection of the grid points of all the regions is finished;
s25, reserving the current grid point in the grid point selection set gamma, entering the next area to select the grid point according to the sequence of small and large internal angle values in the area, generating a grid point selection set again, entering step S22, recording the final grid point selection set if the grid points of all the areas are selected, recording the final grid point selection set as a first grid point selection set, and entering step S26;
s26, after the grid points of all the areas are selected, generating a target reference dictionary matrix FZ according to the first grid point selection set, wherein the expressions of the ith row and the jth column elements of the target reference dictionary matrix FZ are as follows:
FZ i，j ＝A i (α j )，
recycle the productObtaining a migration estimation matrix H by the formed target reference dictionary matrix FZ, wherein H belongs to C M×|Γ| The expression of the ith row and jth column element of the offset estimation matrix H is,
wherein ,Ai ' (. Alpha.) is represented by A i ' (α) derivation of α;
constructing a dictionary expression matrix omega by using a target reference dictionary matrix FZ and an offset estimation matrix H, wherein omega belongs to C M×2|Γ| An expression representing the dictionary matrix is Ω = [ FZ, H]Thereby obtaining a representation dictionary matrix.
4. The method as claimed in claim 3, wherein the method for estimating the incoming wave direction of the single-beat multi-target based on the external radiation source radar,
the step S3 specifically includes:
designing a non-convex substitution function f p (x) The expression is
Wherein x is an independent variable, e is a natural constant, p is a parameter of a non-convex substitution function, and a corresponding pseudo-norm is defined for the vector x
The expression is as follows:
x i for the ith element in the vector x, a non-convex substitution sparse solution model is constructed according to the observation vector and the representation dictionary matrix, wherein the expression is as follows,
thereby constructing and obtaining a non-convex substitution sparse solution model.
5. The method as claimed in claim 4, wherein the method for estimating the incoming wave direction of the single-beat multi-target radar based on external radiation source,
the solving of the non-convex substitution sparse solution model by using the fixed point iterative algorithm specifically comprises the following steps:
s31, randomly generating an initial variable as a current variable;
s32, taking the current variable as input, and substituting the current variable into an optimal solution fixed point expression P (x) to obtain a middle matrix psi, namely psi = P (x), wherein the middle matrix psi is a diagonal matrix, and elements P (x) of the ith row and the ith column of the diagonal matrix i，i Is P (x) i，i ＝|x i |/f′ p (x i), wherein ,xi The i-th element, f 'of an input variable x representing P (x)' p (x i ) Representing a function f for non-convex substitution p () Derivation is carried out; obtaining the current variable x by utilizing the intermediate matrix psi k The calculation formula of the one-time iteration updating value is as follows:
completing one iteration of the current variable;
s33, judging whether the difference value between the current variable and the primary iteration updating value of the current variable is smaller than a convergence threshold value or reaches a set iteration frequency, if the two conditions are not met, taking the primary iteration updating value of the current variable as input, returning to the step S32, and if the two conditions are met, utilizing the variable x obtained by the last iteration updating z The support set S is constructed such that,
represents the variable x z The ith element of (1) toThe support set is used as the constraint of a least square model, a final solution vector is obtained by using the least square model, and the calculation process is as follows:
the final solution x at this time * Namely, the solution vector of the non-convex substitution sparse solution model.
6. The method as claimed in claim 5, wherein the single-shot multi-target incoming wave direction estimation method based on external radiation source radar,
the step S4 specifically includes:
s41, constructing a rationality judgment function g (x), wherein the expression of the rationality judgment function g (x) is as follows:
wherein x is an input vector of the rationality judgment function, and is divided averagely according to the dimension, and x = [ y, z =] T Y is a column vector formed by the first half elements of x, and z is a column vector formed by the second half elements of x;
s42, assuming the resulting first grid point selection set Γ = [ α ] 1 ，α 2 ，.....α G ]G is the number N of the uniformly divided regions of the angle estimation range is the number of elements contained in y, y i Is the ith element in y, z i Is the ith element in z, Δ α i Selecting a minimum spacing, Δ α, for the ith grid point in the set for the first grid point i ＝min(||α i -α i+1 || 2 ，||α i -α i-1 || 2 ) Calculating the final solution x * If the value is less than or equal to the function threshold value
Step S45 is entered;if the final solution x * Is greater than a function threshold
Step S43 is entered;
s43, solving x finally * Dividing the obtained object into x * ＝[y * ，z * ] T ，y * Is x * The column vector z formed by the first half elements of * Is x * The column vector formed by the latter half elements of (a) at y * Selecting the value | y with the maximum rationality i log(y i ) Element y of | i According to the element y i Finding the grid point α in the first grid point selection set Γ corresponding to the serial number, constructing an alternative set based on the grid point, wherein the expression of the constructed alternative set is as follows:
Λ(α*)＝{α|α＝α±k -1 Δα*，k＝1，2，3，4}，
after the candidate set is constructed, replacing the grid points alpha with the grid points in the candidate set Lambda (alpha) one by one, sequentially reconstructing a dictionary expression matrix omega and repeating the step S3 to obtain solution vectors and corresponding rationality judgment function values of the non-convex substitution sparse solving model corresponding to each grid point in the candidate set Lambda (alpha), and judging whether the minimum rationality judgment function value is larger than a function threshold value or not
If it is greater than the function threshold
Step S44 is entered, if the function threshold value is less than or equal to the function threshold value, step S45 is entered;
s44, selecting the grid point with the minimum rationality judgment function value in the alternative set, replacing the grid point alpha, updating the first grid point selection set gamma, reconstructing the expression dictionary matrix omega, repeating the step S3, and solving the final x * Updating, and entering step S43;
s45, utilizing the final solution x * And a first grid point selection set gamma, wherein the estimated value of the wave coming direction of the echo signal of the ith target is obtained by calculation:
θ i ＝α i +z i ，i∈Π，
wherein ,
thereby completing the estimation of the incoming wave direction of the target.
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