Design method of strong interference suppression beam former under multi-target condition
阅读说明：本技术 多目标条件下的强干扰抑制波束形成器设计方法 (Design method of strong interference suppression beam former under multi-target condition ) 是由 白云 刘海嫚 杨鑫 陆路 于 2020-11-30 设计创作，主要内容包括：本发明涉及水声设备设计与制造领域技术领域,具体涉及一种多目标条件下的强干扰抑制波束形成器设计方法,包括以下步骤：S1、设计一个滤波矩阵G∈C～(M×M),使得滤波器输出y(t)＝Gx(t),t＝1,…,N具有空域滤波特性,其中矩阵空域滤波原理；S2、采用稀疏超分辨方位估计算法；S3、基于空域矩阵滤波的稀疏超分辨方位估计：利用空域矩阵滤波和“1”型稀疏近似最小方差算法可以实现强干扰环境下的弱目标的超分辨方位估计；S4、算法的计算机仿真与实测试验数据验证；设计出具有通带和阻带的空间滤波特性的矩阵滤波器,结合高分辨稀疏方位估计算法,从而在信号处理过程中最大程度的实现对干扰的有效抑制,提高声纳对弱目标的检测能力,提高基阵输出信噪比,从而加强声纳的远程探测能力。(The invention relates to the technical field of design and manufacture of underwater acoustic equipment, in particular to a design method of a strong interference suppression beam former under a multi-target condition, which comprises the following steps: s1, designing a filter matrix G e C M×M Such that the filter output y (t) ═ gx (t), t ═ 1, …, N has spatial filtering characteristics, where the matrix spatial filtering principle; s2, adopting a sparse super-resolution orientation estimation algorithm; s3, sparse super-resolution orientation estimation based on spatial matrix filtering: the super-resolution azimuth estimation of a weak target under a strong interference environment can be realized by utilizing space domain matrix filtering and a '1' -type sparse approximate minimum variance algorithm; s4, computer simulation of the algorithm and actual measurement test data verification; designing a matrix filter with pass band and stop band spatial filtering characteristics, combining a high-resolution sparse orientation estimation algorithm, and obtaining a matrix filter with pass band and stop band spatial filtering characteristicsAnd in the signal processing process, the interference is effectively inhibited to the greatest extent, the detection capability of the sonar on the weak target is improved, and the output signal-to-noise ratio of the matrix is improved, so that the remote detection capability of the sonar is enhanced.)
1. A design method of a strong interference rejection beam former under the condition of multiple targets is characterized by comprising the following steps:
s1, designing a filter matrix G e CM×MSuch that the filter output y (t) ═ gx (t), t ═ 1, …, N, has spatial filtering characteristics, where the matrix spatial filtering principle,
the following conditions should be satisfied:
for a known arbitrary geometry matrix consisting of M array elements, D (D) is assumed<M) far-field narrow-band plane wave signal sources from D directions thetaD＝[θ1,…θd…θD]When the array is incident to the array, the narrow-band array signal model received by the M array elements can be expressed as
x(t)＝A(ΘD)s(t)+n(t) (1)；
A (theta) in the formula (1)D)＝[a(θ1),a(θ2),…,a(θD)]Is an M × D dimensional array manifold matrix, s (t) ═ s1(t),s2(t),…,sD(t)]TIs a D x 1 dimensional signal source vector, n (t) is an M x 1 dimensional noise vector,
designing a filter matrix G epsilon C for the formula (1)M×MSo that the filter output y (t) gx (t), t 1, …, N has spatial filtering characteristics, i.e. the filter can suppress the orientation sector signals that are not of interest and pass the orientation sector signals of interest without distortion, the matrix spatial filter should satisfy
Theta in the formula (2)PRepresenting the passband sector, ΘSWhich represents the sector of the stop band,
the filtered output of the matrix filter can be expressed as the narrow-band array signal processing model shown by equation (1)
y(t)＝GHx(t)＝GHA(θ)s(t)+GHn(t),t＝1,…,N (3)；
S2, adopting a sparse super-resolution orientation estimation algorithm:
the necessary conditions for sparse processing are that the number of scanning grid points omega is far larger than the number of array elements M, and the number of array elements M is larger than the number of information sources N, namely omega > M > N,
according to the MVDR power spectrum estimation algorithm, the method can know The parameter estimation can be realized in an iterative mode, the iterative calculation is completed by using an approximate minimum variance algorithm,
the approximate minimum variance algorithm is a method for estimating covariance matrix by using parametersThe minimum, namely the estimation method of the lower bound of the estimation covariance matrix is reached, and the expression is
Cost functionConsistent with the expression of the extended invariant criterion (EXIP), which can be equivalent to an approximate maximum likelihood estimate under large sample conditions,
let r be vec (r), the covariance matrix of the array output data is obtained by vectorization operation
Where vec (-) represents the matrix vectorization operator,representing the Kronecker product, the superscript being the conjugate operator, the matrixSum vectorAre respectively as
According to equation (11), for the k-th parameterIs provided withThen
Order toWill be provided withSubstituting the above formula to obtain the parametersIs estimated as
Using matrix vectorization operationsProduct of KroneckerCan be simplified into
Wherein Tr (-) is matrix tracing operation,
substituting it into formula to implementThe '0' type sparse approximation minimum variance algorithm is obtained by parameter estimation, which is called SAMV-0 for short:
in the formulaRepresenting the covariance matrix estimated at the ith iteration, with its initial valueI.e. the sampling covariance matrixThe initial value of iterative operation can be given by the azimuth spectrum output by the conventional beam former, the iteration cut-off condition is that the error of the estimation of the two iterations is less than a certain preset threshold, and the SAMV-0 algorithm and the iterationThe expression of the adaptive algorithm is consistent if it is to beSubstituting into the formula (16), a '1' type sparse approximation minimum variance algorithm, called SAMV-1 for short, can be obtained:
s3, sparse super-resolution orientation estimation based on spatial matrix filtering:
the super-resolution azimuth estimation of a weak target under a strong interference environment can be realized by utilizing space domain matrix filtering and a '1' -type sparse approximate minimum variance algorithm;
and S4, computer simulation of the algorithm and actual measurement test data verification.
2. The method as claimed in claim 1, wherein in step S1,
the following condition, the least mean square criterion, should also be satisfied:
in general, the array manifold vector in the pass band does not have to be kept completely unchanged after matrix transformation, i.e., the original array manifold can be converted into a virtual array manifold, and at this time, the array manifold vector in the pass band has
In the formulaIs thatA dimension-virtual array manifold vector, or expected response vector, G isDimension matrix, hereNot necessarily equal to M, equation (4) may be written as
Let A ═ A (Θ)p),A(Θs)]，
Solving matrix G can be described as a least mean square criterion design problem:
in the formula | · | non-conducting phosphorFRepresents the Frobenius norm,
the least mean square problem is solved byIn the formula (·)+The pseudo-inverse is represented.
3. The method as claimed in claim 1, wherein in step S1,
the following condition should also be met, the stopband constraint passband Minimax criterion:
discretizing the pass band and stop band orientations respectively to make thetaj∈Θp(j＝1,…,Np) And thetai∈Θs(j＝1,…,Ns) Respectively discretizing the pass band and the stop band sectors, adopting the stop band to restrict the pass band minimum criterion,
the optimization design problem of the stopband constraint passband Minimax criterion matrix filter can be expressed as
s.t.||GHa(θi)||≤ξ0,θi∈Θs,i＝1,…,Ns (7)；
Xi in the formula0For a given attenuation rate of the noise in the stop band sector, the above problem can be solved by converting into a second-order cone programming problem.
4. The method as claimed in claim 1, wherein in step S1,
the following condition should also be satisfied, the stopband constraint passband least mean square criterion:
the optimization design problem of the stopband constraint passband least mean square criterion matrix filter can be expressed as
The problem can be converted into a second-order cone planning form, can be solved by adopting a second-order cone planning method,
5. a method for designing a strong interference suppression beam former under multiple target conditions according to any one of claims 2, 3 or 4, wherein in the step S3,
specifically, the following conditions should also be satisfied,
set at a given frequency f0And the spatial filter characteristic, under the condition thatSpatial matrix filter shown by formula (7)Forming omega azimuth scanning grids by discretizing the azimuth area to form a scanning azimuth set thetaΩAnd as can be seen from equation (16), the covariance matrix of the data after the frequency domain filtering output can be expressed as
Substituting the formula (18) into the formula (17) to obtain a final sparse super-resolution azimuth spectrum estimation result based on spatial matrix filtering
6. The method as claimed in claim 5, wherein in step S4,
specifically, the computer simulation should also satisfy the following conditions:
considering a 36-element uniform linear array, a spatial matrix filter is designed by using the criterion shown in formula (7), and the spatial filtering characteristic of the spatial matrix filter is as follows: the angular sector of the pass band is [ -15 DEG, 15 DEG ]]The stop band angle sector is [ -90 °, -20 ° ]]∪[20°,90°]The linear array element spacing is 2.5m, and the corresponding processing frequency f is under the condition of half-wavelength spacing0The signal power is 300Hz, the stopband attenuation is-25 dB, strong interference exists in the direction of-40 degrees of the spatial direction, the signal power is 15dB, and simultaneously a target signal exists in the directions of-10 degrees and 10 degrees respectively, wherein the former is a moving sound source, the moving sound source moves from the direction of-10 degrees to the direction of 20 degrees in the analysis period, the latter is a fixed sound source, the power of the signal is 0dB, the noise power is 6dB, the system sampling rate is 2000Hz, and the total processing time is 5 min.
7. The method as claimed in claim 6, wherein in step S4,
specifically, the actual measurement test data verifies the effect of the lake test on inhibiting strong interference of the dam power station, and the lake test adopts 7 array elements of an equally spaced linear array with a target direction of 125 degrees.
Technical Field
The invention relates to the technical field of design and manufacture of underwater acoustic equipment, in particular to a design method of a strong interference suppression beam former under a multi-target condition.
Background
Super-resolution azimuth estimation in a strong interference environment is an important research topic in the field of array signal processing such as sonar. For example, in towed-line array sonar, towed-vessel noise is a strong interference source, and its presence can mask or affect the accuracy of positioning underwater targets. The improvement of the target orientation resolution under the strong interference environment condition is the key point of the current research. Matrix filtering techniques are an effective means to achieve known azimuthal strong interference suppression. The matrix filter is firstly proposed and used in the field of frequency filtering, and the Vaccaro gives the design criterion of the frequency domain matrix filter and indicates that the design method is a convex optimization problem. Macinnes solves the matrix filtering design problem by utilizing pseudo-inverse to obtain the least square solution of the matrix filtering design, and the method cannot provide accurate side lobe constraint and transition band range. \37154Thesocial peak converts the convex optimization problem of the matrix filtering design into a second-order cone optimization problem and utilizes sedumi software to effectively solve the problem.
However, in the azimuth estimation under the multi-objective environment, although the conventional positioning method such as the conventional beam forming method (CBF) and the minimum variance distortionless beam forming Method (MVDR) has a certain spatial resolution capability, the beam-tie is ineligible for the positioning problem of the spatial neighboring distribution and the related sound source. In recent years, sparse orientation estimation algorithms have been widely used, such as M-focus, -SVD, and SpSF algorithms. When the number of the azimuth scanning grids is far larger than that of the signals received by the matrix, the signal model has sparsity. The direction estimation capability of the space target can be improved by using the prior information of the sparsity of the signal model.
The remote early warning and detecting capability of the targets is seriously influenced and threatened by factors such as a plurality of sea-surface targets, high interference intensity, wide coverage range and the like in important navigation channels (ports) and complex combat areas.
Based on this background, the design of how to suppress the beamformer by high-gain interference in the multi-objective, strong interference background is studied.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for designing a strong interference suppression beam former under the condition of multiple targets, which designs a matrix filter with the spatial filtering characteristics of a pass band and a stop band by utilizing a matrix filtering technology, and combines a high-resolution sparse orientation estimation algorithm, thereby realizing the effective suppression of interference to the maximum extent in the signal processing process, improving the detection capability of sonar on weak targets, improving the output signal-to-noise ratio of a matrix and further strengthening the remote detection capability of the sonar. The method has very important practical significance for improving and upgrading the active shore-based sonar or developing a novel sonar model.
The invention is realized by the following technical scheme:
a design method of a strong interference rejection beam former under the condition of multiple targets comprises the following steps:
s1, designing a filter matrix G e CM×MSuch that the filter output y (t) ═ gx (t), t ═ 1, …, N, has spatial filtering characteristics, where the matrix spatial filtering principle,
the following conditions should be satisfied:
for a known arbitrary geometry matrix consisting of M array elements, D (D) is assumed<M) far-field narrow-band plane wave signal sources from D directions thetaD＝[θ1,…θd…θD]When the array is incident to the array, the narrow-band array signal model received by the M array elements can be expressed as
x(t)＝A(ΘD)s(t)+n(t) (1)；
A (theta) in the formula (1)D)＝[a(θ1),a(θ2),…,a(θD)]Is an M × D dimensional array manifold matrix, s (t) ═ s1(t),s2(t),…,sD(t)]TIs a D x 1 dimensional signal source vector, n (t) is an M x 1 dimensional noise vector,
designing a filter matrix G epsilon C for the formula (1)M×MThe filter output y (t) gx (t), t 1, …, N has spatial filtering characteristics, i.e. the filter can suppress the orientation sector signals that are not of interest and make them of interestThe interested azimuth sector signal passes through without distortion, and the matrix spatial filter satisfies
Theta in the formula (2)PRepresenting the passband sector, ΘSWhich represents the sector of the stop band,
the filtered output of the matrix filter can be expressed as the narrow-band array signal processing model shown by equation (1)
y(t)＝GHx(t)＝GHA(θ)s(t)+GHn(t),t＝1,…,N (3)；
S2, adopting a sparse super-resolution orientation estimation algorithm:
the necessary conditions for sparse processing are that the number of scanning grid points omega is far larger than the number of array elements M, and the number of array elements M is larger than the number of information sources N, namely omega > M > N,
according to the MVDR power spectrum estimation algorithm, the method can know The parameter estimation can be realized in an iterative mode, the iterative calculation is completed by using an approximate minimum variance algorithm,
the approximate minimum variance algorithm is a method for estimating covariance matrix C by using parametersPThe minimum, namely the estimation method of the lower bound of the estimation covariance matrix is reached, and the expression is
Cost functionConsistent with the expression of the extended invariant criterion (EXIP), which can be equivalent to an approximate maximum likelihood estimate under large sample conditions,
let r be vec (r), the covariance matrix of the array output data is obtained by vectorization operation
Where vec (-) represents the matrix vectorization operator,representing the Kronecker product, the superscript being the conjugate operator, the matrixSum vectorAre respectively as
According to equation (11), for the k-th parameterIs provided withThen
Order toWill be provided withSubstituting the above formula to obtain the parametersIs estimated as
Using matrix vectorization operationsProduct of KroneckerCan be simplified into
Wherein Tr (-) is matrix tracing operation,
substituting it into formula to implementThe '0' type sparse approximation minimum variance algorithm is obtained by parameter estimation, which is called SAMV-0 for short:
in the formulaRepresenting the covariance matrix estimated at the ith iteration, with its initial valueI.e. the sampling covariance matrixThe initial value of the iterative operation can be given by the output azimuth spectrum of the conventional beam former, and the iterative cutoff condition is two times before and afterIf the iterative estimation error is less than a certain preset threshold, the expressions of the SAMV-0 algorithm and the iterative adaptive algorithm are consistent, if the iterative estimation error is less than the certain preset threshold, the expressions of the SAMV-0 algorithm and the iterative adaptive algorithm are consistentSubstituting into the formula (16), a '1' type sparse approximation minimum variance algorithm, called SAMV-1 for short, can be obtained:
s3, sparse super-resolution orientation estimation based on spatial matrix filtering:
the super-resolution azimuth estimation of a weak target under a strong interference environment can be realized by utilizing space domain matrix filtering and a '1' -type sparse approximate minimum variance algorithm;
and S4, computer simulation of the algorithm and actual measurement test data verification.
Preferably, in the step S1,
the following condition, the least mean square criterion, should also be satisfied:
in general, the array manifold vector in the pass band does not have to be kept completely unchanged after matrix transformation, i.e., the original array manifold can be converted into a virtual array manifold, and at this time, the array manifold vector in the pass band has
In the formulaIs thatA dimension-virtual array manifold vector, or expected response vector, G isDimension matrix, hereNot necessarily equal to M.
Equation (4) can be written as
Order to
Solving matrix G can be described as a least mean square criterion design problem:
in the formula | · | non-conducting phosphorFRepresents the Frobenius norm,
the least mean square problem is solved byIn the formula (·)+The pseudo-inverse is represented.
Preferably, in the step S1,
the following condition should also be met, the stopband constraint passband Minimax criterion:
discretizing the pass band and stop band orientations respectively to make thetaj∈Θp(j＝1,…,Np) And thetai∈Θs(j＝1,…,Ns) Respectively discretizing the pass band and the stop band sectors, adopting the stop band to restrict the pass band minimum criterion,
the optimization design problem of the stopband constraint passband Minimax criterion matrix filter can be expressed as
Xi in the formula0For a specified attenuation rate of the noise in the stop band sectorThe problem can be solved as a second-order cone programming problem through conversion.
Preferably, in the step S1,
the following condition should also be satisfied, the stopband constraint passband least mean square criterion:
the optimization design problem of the stopband constraint passband least mean square criterion matrix filter can be expressed as
The problem can be converted into a second-order cone planning form, can be solved by adopting a second-order cone planning method,
preferably, in the step S3,
specifically, the following conditions should also be satisfied,
set at a given frequency f0And the spatial domain matrix filter shown in the formula (7) is used under the condition of spatial filtering characteristicsForming omega azimuth scanning grids by discretizing the azimuth area to form a scanning azimuth set thetaΩAnd as can be seen from equation (16), the covariance matrix of the data after the frequency domain filtering output can be expressed as
Substituting the formula (18) into the formula (17) to obtain a final sparse super-resolution azimuth spectrum estimation result based on spatial matrix filtering
Preferably, in the step S4,
specifically, the computer simulation should also satisfy the following conditions:
considering a 36-element uniform linear array, a spatial matrix filter is designed by using the criterion shown in formula (7), and the spatial filtering characteristic of the spatial matrix filter is as follows: the angular sector of the pass band is [ -15 DEG, 15 DEG ]]The stop band angle sector is [ -90 °, -20 ° ]]∪[20°,90°]The linear array element spacing is 2.5m, and the corresponding processing frequency f is under the condition of half-wavelength spacing0Is 300 Hz. The attenuation amount of the stop band is-25 dB, strong interference exists in the direction of-40 degrees of the spatial direction, the signal power of the strong interference is 15dB, and simultaneously a target signal exists in the directions of-10 degrees and 10 degrees respectively, wherein the former is a moving sound source and moves from the direction of-10 degrees to the direction of 20 degrees in an analysis period, the latter is a fixed sound source, the power of the signal is 0dB, the noise power is 6dB, the sampling rate of the system is 2000Hz, and the total processing time is 5 min.
Preferably, in the step S4,
specifically, the actual measurement test data verifies the effect of the lake test on inhibiting strong interference of the dam power station, and the lake test adopts 7 array elements of an equally spaced linear array with a target direction of 125 degrees.
The invention has the beneficial effects that:
the interference suppression beam forming algorithm under the multi-target condition, which is designed by the invention, utilizes the matrix spatial filtering technology to carry out spatial filtering on array data, the filtering output still keeps the data characteristic of an array element domain, and the algorithm can play the aims of purifying data, improving the signal-to-noise ratio and improving the subsequent processing performance as a spatial pre-filter. The matrix spatial filtering technology is combined with the high-resolution sparse orientation estimation technology, and the method has the following advantages:
1) under the strong interference environment, the strong interference signal of the known direction is effectively inhibited, and the energy of the target signal of interest is reserved without distortion;
2) under the strong interference environment, the azimuth resolution capability of the space target is improved;
3) the super-resolution azimuth estimation of the weak target under the strong interference environment is realized, and the detection performance of the weak target is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a spatial response amplitude plot of a matrix filter in accordance with the present invention;
FIG. 2 is a diagram of the interference suppression preamble in the present invention;
FIG. 3 is a diagram of the azimuth history after interference suppression according to the present invention;
FIG. 4 is a processing result at a time before interference suppression according to the present invention;
fig. 5 shows the processing result at a certain time after the interference suppression in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
the invention specifically discloses a technical scheme of a design method of a strong interference rejection beam former under a multi-target condition, which comprises the following steps:
s1, designing a filter matrix G e CM×MSuch that the filter output y (t) ═ gx (t), t ═ 1, …, N, has spatial filtering characteristics, where the matrix spatial filtering principle,
the following conditions should be satisfied:
for a known arbitrary geometry matrix consisting of M array elements, D (D) is assumed<M) far-field narrow-band plane wave signal sources from D directions thetaD＝[θ1,…θd…θD]When the array is incident to the array, the narrow-band array signal model received by the M array elements can be expressed as
x(t)＝A(ΘD)s(t)+n(t) (1)；
A (theta) in the formula (1)D)＝[a(θ1),a(θ2),…,a(θD)]Is an M × D dimensional array manifold matrix, s (t) ═ s1(t),s2(t),…,sD(t)]TIs a D x 1 dimensional signal source vector, n (t) is an M x 1 dimensional noise vector,
designing a filter matrix G epsilon C for the formula (1)M×MSo that the filter output y (t) gx (t), t 1, …, N has spatial filtering characteristics, i.e. the filter can suppress the orientation sector signals that are not of interest and pass the orientation sector signals of interest without distortion, the matrix spatial filter should satisfy
Theta in the formula (2)PRepresenting the passband sector, ΘSWhich represents the sector of the stop band,
the filtered output of the matrix filter can be expressed as the narrow-band array signal processing model shown by equation (1)
y(t)＝GHx(t)＝GHA(θ)s(t)+GHn(t),t＝1,…,N (3)；
S2, adopting a sparse super-resolution orientation estimation algorithm:
the necessary conditions for sparse processing are that the number of scanning grid points omega is far larger than the number of array elements M, and the number of array elements M is larger than the number of information sources N, namely omega > M > N,
according to the MVDR power spectrum estimation algorithm, the method can know The parameter estimation can be realized in an iterative way, and the calculation of (2) is supposed to be carried out hereThe iterative computation is done with an approximate minimum variance algorithm,
the approximate minimum variance algorithm is a method for estimating covariance matrix by using parametersThe minimum, namely the estimation method of the lower bound of the estimation covariance matrix is reached, and the expression is
Cost functionConsistent with the expression of the extended invariant criterion (EXIP), which can be equivalent to an approximate maximum likelihood estimate under large sample conditions,
let r be vec (r), the covariance matrix of the array output data is obtained by vectorization operation
Where vec (-) represents the matrix vectorization operator,representing the Kronecker product, the superscript being the conjugate operator, the matrixSum vectorAre respectively as
According to equation (11), for the k-th parameterIs provided withThen
Order toWill be provided withSubstituting the above formula to obtain the parametersIs estimated as
Using matrix vectorization operationsProduct of KroneckerCan be simplified into
Wherein Tr (-) is matrix tracing operation,
substituting it into formula to implementObtaining the 0 type sparse approximate minimum squareDifference algorithm, SAMV-0 for short:
in the formulaRepresenting the covariance matrix estimated at the ith iteration, with its initial valueI.e. the sampling covariance matrixThe initial value of Iterative operation can be given by the azimuth spectrum output by a conventional beam former, the iteration cut-off condition is that the error of the estimation of the two iterations is less than a certain preset threshold, and the expressions of SAMV-0 algorithm and Iterative Adaptive Algorithm (IAA) are consistent as known by reference to related documents, if the expressions are to be given, the initial value of Iterative operation is given by the azimuth spectrum output by the conventional beam former, and the iteration cut-off condition is that the error of the estimation of the two iterations is less than aSubstituting into the formula (16), a '1' type sparse approximation minimum variance algorithm, called SAMV-1 for short, can be obtained:
s3, sparse super-resolution orientation estimation based on spatial matrix filtering:
the 1-type sparse approximate minimum variance algorithm can effectively realize super-resolution azimuth estimation, when a strong interference source exists in the environment, the strong interference can mask the existence of a target or influence the positioning precision of the target, and the super-resolution azimuth estimation of a weak target in the strong interference environment can be realized by utilizing spatial matrix filtering and the 1-type sparse approximate minimum variance algorithm;
and S4, computer simulation of the algorithm and actual measurement test data verification.
Further, in step S1,
the following condition, the least mean square criterion, should also be satisfied:
in general, the array manifold vector in the pass band does not have to be kept completely unchanged after matrix transformation, i.e., the original array manifold can be converted into a virtual array manifold, and at this time, the array manifold vector in the pass band has
In the formulaIs thatA dimension-virtual array manifold vector, or expected response vector, G isDimension matrix, hereNot necessarily equal to M.
Equation (4) can be written as
Let A ═ A (Θ)p),A(Θs)]，
Solving matrix G can be described as a least mean square criterion design problem:
in the formula | · | non-conducting phosphorFRepresents the Frobenius norm,
the least mean square problem is solved byIn the formula (·)+The pseudo-inverse is represented.
Further, in step S1,
the following condition should also be met, the stopband constraint passband Minimax criterion:
discretizing the pass band and stop band orientations respectively to make thetaj∈Θp(j＝1,…,Np) And thetai∈Θs(j＝1,…,Ns) Respectively discretizing the pass band and the stop band sectors, adopting the stop band to restrict the pass band minimum criterion,
the optimization design problem of the stopband constraint passband Minimax criterion matrix filter can be expressed as
Xi in the formula0For a given attenuation rate of the noise in the stop band sector, the above problem can be solved by converting into a second-order cone programming problem.
Further, in step S1,
the following condition should also be satisfied, the stopband constraint passband least mean square criterion:
the optimization design problem of the stopband constraint passband least mean square criterion matrix filter can be expressed as
The problem can be converted into a second-order cone planning form, can be solved by adopting a second-order cone planning method,
further, in step S3,
specifically, the following conditions should also be satisfied,
set at a given frequency f0And the spatial domain matrix filter shown in the formula (7) is used under the condition of spatial filtering characteristicsForming omega azimuth scanning grids by discretizing the azimuth area to form a scanning azimuth set thetaΩAnd as can be seen from equation (16), the covariance matrix of the data after the frequency domain filtering output can be expressed as
Substituting the formula (18) into the formula (17) to obtain a final sparse super-resolution azimuth spectrum estimation result based on spatial matrix filtering
Further, in step S4,
specifically, the computer simulation should also satisfy the following conditions:
considering a 36-element uniform linear array, a spatial matrix filter is designed by using the criterion shown in formula (7), and the spatial filtering characteristic of the spatial matrix filter is as follows: the angular sector of the pass band is [ -15 DEG, 15 DEG ]]The stop band angle sector is [ -90 °, -20 ° ]]∪[20°,90°]The linear array element spacing is 2.5m, and the corresponding processing frequency f is under the condition of half-wavelength spacing0Is 300 Hz. The attenuation amount of the stop band is-25 dB, strong interference exists in the direction of-40 degrees of the spatial direction, the signal power of the strong interference is 15dB, and simultaneously a target signal exists in the directions of-10 degrees and 10 degrees respectively, wherein the former is a moving sound source and moves from the direction of-10 degrees to the direction of 20 degrees in an analysis period, the latter is a fixed sound source, the power of the signal is 0dB, the noise power is 6dB, the sampling rate of the system is 2000Hz, and the total processing time is 5 min.
The spatial domain amplitude response of the matrix spatial domain filter obtained by design is drawn in figure 1, and as can be seen from the figure, the spatial domain response of the matrix spatial domain filter obtained by design meets the design requirement, the filtering response of the spatial domain in a pass band is 0dB, the stop band part is strictly controlled below-25 dB, and the spatial domain responses of all analysis frequency points are kept consistent. Fig. 2 is the result of interference suppression before CBF algorithm, where there are three target orientations, resulting in two relatively weak target signals near the right lateral direction being easily swamped by background noise due to strong interference in the-40 ° direction. Fig. 3 is a diagram of the azimuth history after interference suppression in the CBF algorithm, and it can be seen that strong interference in the-40 ° direction is completely suppressed. Because the matrix filter filters the interference with stronger energy, the relative energy value of the weak target signal becomes higher, and the motion angle track on the BTR graph is more prominent.
Further, in step S4,
specifically, the actual measurement test data verifies the effect of the lake test on inhibiting strong interference of the dam power station, and the lake test adopts 7 array elements of an equally spaced linear array with a target direction of 125 degrees.
Fig. 4 shows the beam forming result at a certain time before interference suppression, and it can be seen that a strong interference target located at 60 ° azimuth is a dam power station, and the energy of the strong interference target is higher than the target energy. Fig. 5 shows the beamforming result at a certain time after applying interference suppression, the strong interference in the 60 ° direction is completely suppressed, and the weak target signal is correspondingly enhanced. Meanwhile, matrix spatial filtering is combined with a super-resolution estimation algorithm, and compared with a CBF algorithm, the signal processing gain and the azimuth resolution are improved.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.