CN109188342A - Low complex degree arrival direction estimation method under conformal circle battle array - Google Patents

Low complex degree arrival direction estimation method under conformal circle battle array Download PDF

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CN109188342A
CN109188342A CN201810815428.XA CN201810815428A CN109188342A CN 109188342 A CN109188342 A CN 109188342A CN 201810815428 A CN201810815428 A CN 201810815428A CN 109188342 A CN109188342 A CN 109188342A
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array
conformal
battle array
array element
local
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张小飞
周梦婕
沈金清
弓盼
汪云飞
郑旺
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received

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Abstract

The invention discloses a kind of low complex degree arrival direction estimation methods under conformal round battle array, obtain receiving the signal subspace of data using PASTd method, it is then based on dimensionality reduction MUSIC algorithm and the four-dimensional spectrum peak search of conformal round battle array is down to two-dimentional spectrum peak search, realize the low complex degree DOA estimation under conformal round battle array.The invention has the benefit that the DOA algorithm for estimating based on dimensionality reduction MUSIC under the conformal round battle array of comparison, inventive algorithm complexity is low, is conducive to hardware realization；The DOA algorithm for estimating based on PAST under conformal round battle array is compared, there is the present invention better DOA to estimate performance.

Description

Low complex degree arrival direction estimation method under conformal circle battle array
Technical field
Low complex degree two dimension DOA the present invention relates to array signal processing technology, under especially a kind of conformal round battle array Estimation method.
Background technique
With the increasingly raising that people require target location accuracy, traditional direction finding side using wave beam mechanical scanning Method has all been unable to satisfy the requirement of practical application in speed, precision and resolution ratio, and being widely used for conformal array not only may be used To save space, influence of the antenna to vehicle aerodynamics performance is reduced to the maximum extent, it can be with extended antenna wave beam Scanning range effectively improves Electro Magnetic Compatibility.It is different from classical linear array, face battle array, due to being influenced by conformal carrier curvature, The element pattern direction of conformal array antenna is inconsistent, multipolarization characteristic is showed, so that the number of snapshots of conformal array antenna The polarization parameter of array incoming signal is introduced when according to modeling.Therefore, the coupling of information source orientation and polarized state is under conformal array The difficult point of high resolution DOA estimation.Currently, being concentrated mainly on guiding to the existing research of conformal array high resolution DOA estimation method Classic algorithm transplanting under the conditions of Vector Modeling and simplified model.The present invention is for this kind of special conformal array junctions of conformal round battle array Structure proposes the blind polarization DOA algorithm for estimating of low complex degree under the array, realizes accurate DOA estimation.
Summary of the invention
Technical problem to be solved by the present invention lies in provide the low complex degree arrival direction estimation under the conformal round battle array of one kind Method, the low complex degree DOA that can be realized under conformal round battle array accurately estimate.
In order to solve the above technical problems, the present invention provides the low complex degree arrival direction estimation method under the conformal round battle array of one kind, Include the following steps:
(1) the global rotation transformation for realizing array elements polarization direction figure is rotated using Euler, solves conformal array antenna Multipolarization problem, to construct the array data model under conformal round battle array；
(2) signal subspace of array received signal is obtained based on PASTd method；
(3) according to the design feature of spectral function, four-dimensional MUSIC spectrum peak search is down to two-dimentional MUSIC spectrum peak search, is realized Low complex degree arrival direction estimation under conformal circle battle array.
Preferably, step (1) specifically:
The steering vector of conformal antenna is codetermined by incoming signal parameter (θ, φ, γ, η), wherein γ, η are incident letter Number polarization parameter, θ, φ are pitch angle and the azimuth of incoming signal, and one is made of M identical omnidirectional arrays Uniform circular array, direction matrix are as follows:
Since the definition and design of general array element directional diagram are all using local local coordinate system as reference, it is therefore desirable to benefit The global rotation transformation for realizing array element polarization direction figure is rotated with Euler, i.e., by local array element directional diagramBe converted to the overall situation Array element directional diagram gmThe shift step of (θ, φ), each array element are as follows:
(11) unit vector in global coordinate system at (θ, φ) is subjected to rectangular co-ordinate expression:
X=sin θ cos φ, y=sin θ sin φ, z=cos θ
(12) by the local rectangular coordinates of global rectangular coordinates transformation to array element and part is obtained using Euler's rotation transformation Corresponding orientation in polar coordinatesRotation transformation Eulerian angles corresponding with array structure and Euler's rotational transformation matrix difference Is defined as:
Dm=2 (m-1) π/M, Em=0, Fm=0
(13) it is responded by the local polar coordinates of array elementObtain its expression under local rectangular coordinate system:
In formula,It is indicated for the polarization of m-th of array element directional diagram under local coordinate system, and There are following relationships:
(14) it is indicated by the local rectangular coordinate system of array element directional diagram and Euler rotates inverse transformation and obtains array element directional diagram Global rectangular co-ordinate indicate:
(15) the array element directional diagram under global rectangular co-ordinate is finally converted into global polar coordinate representation, obtains gmθ,gmφ:
gmθ(θm,φm)=- gmZ/sinθ
gmφ(θm,φm)=- gmXsinφ+gmYcosφ
Therefore, the receipt signal model of array are as follows:
In formula,To receive data vector,For incoming signal vector；It makes an uproar for array Acoustic vector.
Preferably, step (2) specifically:
(21) initial value λ appropriate is selectedn(0), (0) W；
(22) to each t=1,2 ..., J (J is number of snapshots), so that x1(t)=X (t)；
(23) following variable: array received number is updated respectively to each n=1,2 ..., N (N is information source number) Characteristic valueFeature vector And array received data xn+1(t)=xn(t)-Wn(t)yn(t)；
(24) after the n=N in step (23), so that t=t+1, calculates since step (22) again；PASTd algorithm Final step passes through xn(t) n-th of characteristic vector W of C (t) is subtractedn(t) reach algorithm deflation.
Preferably, step (3) specifically:
According to the rudimentary knowledge of array signal processing, defining array manifold spectral function is
It will be in above formulaIt is rewritten into
It enablesThen compose letter Number can be write as
It enablesEasily card Q (θ, φ) be positive semidefinite matrix, and if only if (θ, φ)= (θi,φi), when i=1,2 ..., N, Q (θ, φ) is singular matrix, i.e. Q (θ, φ) is unusual at the true incident direction of information source, There is det (Q (θ to matrix Q (θ, φ) at this timei,φi))=0, i=1 ..., N, it can thus be concluded that the DOA estimation spectrum letter of conformal circle battle array Number
Carrying out two-dimensional search using above formula can be obtained the DOA information of incoming signal.
The invention has the benefit that the DOA algorithm for estimating based on dimensionality reduction MUSIC under the conformal round battle array of comparison, the present invention calculate Method complexity is low, is conducive to hardware realization；The DOA algorithm for estimating based on PAST under conformal round battle array is compared, the present invention has better DOA estimates performance.
Detailed description of the invention
Fig. 1 is array structure schematic diagram of the invention.
Fig. 2 is the perspective view of incoming signal polarization of the invention in array element polarization direction figure.
Fig. 3 is PASTd algorithm flow schematic diagram of the invention.
Fig. 4 is the RMSE performance comparison schematic diagram of each algorithm of the present invention under different signal-to-noise ratio.
Fig. 5 is the RMSE performance comparison schematic diagram of each algorithm of the present invention under different number of snapshots.
Fig. 6 is the RMSE performance comparison schematic diagram of algorithm of the invention under different array numbers.
Specific embodiment
Symbol: small letter (capitalization) boldface letter indicates vector (matrix).(·)T、(·)HRespectively indicate matrix or vector Transposition, conjugate transposition.E () is statistical expection.⊙ indicates Hadamard product operation.Diag () represents the element for using vector Diagonal matrix as diagonal element.Angle () expression takes phase angle.Triu () expression takes triangle element on matrix.Table Show the estimation to value x.
The present invention is defined as follows coordinate system: [x, y, z] indicates array overall situation rectangular co-ordinate,Indicate that array element is locally straight Angular coordinate, [r, θ, φ] indicate array element overall situation polar coordinates,Indicate array element part polar coordinates.
One, data model
The array structure of conformal circle battle array is as shown in Figure 1, M identical omnidirectional arrays are evenly distributed on plane X-Y upper one Radius is on the circumference of R.Angle between adjacent two array element is β=2 π/M, and array element serial number m sorts counterclockwise, m-th gust The angle of line and X-axis between first concentric are as follows:
Its position vector is rm=(Rcos δm,Rsinδm,0)。
The direction of arrival of incident plane wave is indicated using spheric coordinate system herein, the origin O of coordinate system is at the center of array That is the center of circle.The pitch angle θ ∈ [0, pi/2] of information source is the angle of Z axis Yu information source incident direction, azimuth φ ∈ [0,2 π] be then from The angle that X-axis projects on array plane of incidence to information source incident direction in the counterclockwise direction.Equipped with N number of narrow band signal source from remote Field is radiated aerial array, and n-th of information source angle of arrival is (θn,φn)。
Due to the rotation relationship of the rotation relationship of array element coordinate system and polarization components in conformal antenna array, so that conformal day The steering vector of line is codetermined by incoming signal parameter (θ, φ, γ, η).Wherein, γ, η are the polarization parameter of incoming signal, It is specifically defined are as follows: be at any time in the endpoint for propagating electric field intensity on cross section of the point for any point on the direction of propagation Between a polarization ellipse changing, elliptical shape, inclination angle and rotation direction depend on both direction electromagnetic field magnitude ratio and phase Difference.Definition, tan γ=Ax/AyIndicate the electric field amplitude of Y-direction and the electric field amplitude ratio of X-direction, η=φy-φxIndicate Y-direction The phase difference of electric field and X-direction electric field, value range be γ ∈ [0, pi/2], η ∈ [0,2 π).Therefore for shown in FIG. 1 conformal Circle battle array, direction matrix are as follows:
Wherein polarization components P (γ, η)=[p (γ1,η1),p(γ2,η2),…,p(γN,ηN)], direction vector If using pmi(m=1 ..., M) indicate the polarization vector of i-th of incoming signal in m Projection on the polarization direction figure of a array element, as shown in Fig. 2, then
p(γi,ηi)=[p1i,p2i,…,pMi]T
In formula, pmi=ui·gm, gmThe orthogonally polarized component for being m-th of array element directional diagram in global coordinate system indicates.EθAnd EφFor cross polarization base vector in global coordinate system；WithExist for i-th of incoming signal polarization Cross polarization exploded representation in global coordinate system,
General array element directional diagramDefinition and design be all using local local coordinate system as refer to, i.e., Indicate directional diagram of m-th of the array element in local coordinate system, it is therefore desirable to rotate using Euler and realize array element polarization direction figure Global rotation transformation, i.e., by local array element directional diagramBe converted to global array element directional diagram gm(θ,φ).Therefore gmIt indicates Are as follows:
gm=gmθEθ+gmφEφ
In formula, gmθ,gmφFor the global rotation transformation for rotating the array element polarization direction figure realized using Euler, indicate m-th Orthogonally polarized component of the array element directional diagram in global coordinate system.The shift step of each array element is as follows:
Unit vector in global coordinate system at (θ, φ) is carried out rectangular co-ordinate expression by step 1:
X=sin θ cos φ, y=sin θ sin φ, z=cos θ
Step 2 by the local rectangular coordinates of global rectangular coordinates transformation to array element and obtains part using Euler's rotation transformation Corresponding orientation in polar coordinatesRotation transformation Eulerian angles corresponding with Fig. 1 array structure and Euler's rotational transformation matrix It is respectively defined as:
Dm=2 (m-1) π/M, Em=0, Fm=0
Step 3 is responded by the local polar coordinates of array elementObtain its expression under local rectangular coordinate system:
In formula,It is indicated for the polarization of m-th of array element directional diagram under local coordinate system, and There are following relationships:
Step 4 is indicated by the local rectangular coordinate system of array element directional diagram and Euler rotates inverse transformation and obtains array element directional diagram Global rectangular co-ordinate indicate:
Array element directional diagram under global rectangular co-ordinate is finally converted into global polar coordinate representation by step 5, obtains gmθ,gmφ:
gmθ(θm,φm)=- gmZ/sinθ
gmφ(θm,φm)=- gmXsinφ+gmYcosφ
Therefore, the receipt signal model of array are as follows:
In formula,To receive data vector,For incoming signal vector；It makes an uproar for array Acoustic vector.
Two, noise subspace is obtained using PASTd method
One is defined without constraint cost function
It can be found that
E{xHWWHX }=tr (E { WHxxHW })=tr (WHCW)
E{xHWWHWWHX }=tr (E { WHWxxHWHW })=tr (WHCWWHW)
Wherein C indicates to receive the autocorrelation matrix of data x.Assuming that W order is N, then J (W) can be indicated are as follows:
J (W)=tr (C) -2tr (WHCW)+tr(WHCWWHW)
Bin Yang proposes the important theorem of following two: theorem 1:W is an equalization point of J (W), and if only if W= UrQ,UrIt is the matrix of M × N, Q is any unitary matrice of N × N.Feature vector is not in matrix UrCharacteristic value and as J (W) Value.Theorem 2: only UrIt is in the case that N number of main feature vector of Matrix C forms, objective function J (W) obtains minimum.? In any other situation, the equalization point of J (W) is all saddle point.It is known that by the above theorem when objective function J (W) minimalization When, the column space of W is equivalent to signal subspace.
In reality, in order to update to obtain the subspace W (t) of t moment, the subspace W using the t-1 moment is needed (t-1) and the array element data x (t) of t moment.We select gradient descent method herein, choose downward gradient and are
So
Wherein, μ > 0 indicates the step value for needing suitably to select.By C (t)=x (t) xH(t), y (t)=WH(t-1) x (t) generation Enter above formula, obtains
W (t)=W (t-1)-μ [2x (t) yH(t)-x(t)yH(t)
×WH(t-1)W(t-1)-W(t-1)WH(t-1)y(t)yH(t)]
When obtaining minimum due to J (W), WH(t-1) W (t-1)=I, can obtain
W (t)=W (t-1)+μ [x (t)-W (t-1) y (t)] yH(t)
The ability of invariant subspace is poor when due to W (t) tracking, and algorithmic statement is slow.In order to solve this problem it can define One new exponential weighting function
Wherein 0 < β≤1 indicates forgetting factor, mainly guarantees that past data are reduced weight under unstable environment, To guarantee the stability of tracking.Common sliding window is corresponded to as β=1.Further, it is possible to Think
Y (i)=WH(i-1)x(i)≈WH(t)x(i)
Therefore modified objective function is obtained
When objective function global minima, W (t) can use autocorrelation matrix Cyy(t) and cross-correlation matrix Cxy(t) carry out table Show, minJ (W (t)) optimal solution is Wiener filter, i.e.,
Wherein, Cyy(t) and Cxy(t) more new formula are as follows:
PASTd method is mainly using deflation technology by centainly sequentially estimating principal component, first when number of targets N is 1 Current most important characteristic vector W is estimated by PAST methodn(t), then the data x of current t momentn(t) it is subtracted in spy Levy vector Wn(t) projection on obtains xn+1(t), it then repeats the above steps and calculates Wn+1(t),Wn+2(t)…。
Solving source signal subspace using PASTd method, specific step is as follows:
1) initial value λ appropriate is selectedn(0), (0) W；
2) to each t=1,2 ..., J (J is number of snapshots), so that x1(t)=X (t)；
3) following variable: array received number y is updated respectively to each n=1,2 ..., N (N is information source number)n(t)=Characteristic valueFeature vector And array received data xn+1(t)=xn(t)-Wn(t)yn(t)；
4) after the n=N in step (3), so that t=t+1, calculates since step (2) again；
The algorithm flow chart of PASTd is as shown in figure 3, algorithm final step passes through xn(t) subtract n-th of feature of C (t) to Measure Wn(t) reach algorithm deflation.
Three, spectrum peak search obtains DOA information
Noise subspace U is obtained by PASTd algorithmN, by the rudimentary knowledge of array signal processing it is found that array steering vector The subspace opened is orthogonal with noise subspace.Therefore defining array manifold spectral function is
It will be in above formulaIt is rewritten into
It enablesThen compose letter Number can be write as
It enablesObviously there is Q (θi,φi)=QH(θi,φi), due to p (γi,ηi) For non-vanishing vector, p (γi,ηi) ≠ 0, as parameter (θ, φ, γ, η)=(θi,φi,γi,ηi), when i=1,2 ..., N, haveThere is p at this timeH(γi,ηi)Q(θi,φi)p(γi,ηi)=0；As parameter (θ, φ, γ, η) ≠ (θi, φi,γi,ηi), when i=1,2 ..., N,pH(γi,ηi)Q(θi,φi)p(γi,ηi)>0.Therefore Q (θ, φ) is positive semidefinite matrix, and if only if (θ, φ)=(θi,φi), when i=1,2 ..., N, Q (θ, φ) is singular matrix, i.e., Q (θ, φ) is unusual at the true incident direction of information source, has det (Q (θ to matrix Q (θ, φ) at this timei,φi))=0, i= 1,...,N.It can thus be concluded that the DOA of conformal circle battle array estimates spectral function
Carrying out two-dimensional search using above formula can be obtained the DOA information of incoming signal.
Algorithm performance of the invention is analyzed below with MATLAB emulation.Wherein, using rooting mean square error (Root Mean Square Error, RMSE) carrys out assessment algorithm DOA estimation performance, and RMSE is defined as follows:
Wherein, the information source number in N representation space, L indicate Monte Carlo test number (TN).WithRespectively indicate q N-th of information source elevation angle theta when secondary Monte Carlo is testednAnd azimuth φnEstimated value,WithRespectively indicate its exact value.
Table 1 is algorithm complexity comparison.Wherein, uv indicates spectrum peak search number.Complexity of the invention as can be seen from Table 1 Degree is lower than the complexity for carrying out DOA estimation based on dimensionality reduction MUSIC.
The comparison of 1 algorithm complexity of table
Conformal round battle array algorithm for estimating based on dimensionality reduction MUSIC O{M3+M2J+(M3+M+1)uv}
Algorithm proposed by the present invention O{(4MN+N)J+(M2+M+1)uv}
Fig. 4 is the RMSE performance comparison figure of each algorithm under different signal-to-noise ratio.Wherein, array number M=7, number of snapshots J= 300, information source number K=2, the direction of incoming signal are respectively (20 °, 5 °), (40 °, 25 °).From fig. 4, it can be seen that of the invention RMSE performance is improved with the increase of signal-to-noise ratio, and better than the conformal round battle array DOA algorithm for estimating based on PAST.
Fig. 5 is the RMSE performance comparison figure of each algorithm under different number of snapshots.Wherein, array number M=7, signal-to-noise ratio are 20dB, information source number K=2, the direction of incoming signal are respectively (20 °, 5 °), (40 °, 25 °).From fig. 5, it can be seen that of the invention RMSE performance is improved with the increase of number of snapshots, and better than the conformal round battle array DOA algorithm for estimating based on PAST.
Fig. 6 is performance comparison figure of the present invention under different array numbers.Wherein, signal-to-noise ratio 20dB, information source number K=2, fastly Umber of beats J=300, the direction of incoming signal are respectively (20 °, 5 °), (40 °, 25 °).Fig. 6 show RMSE performance of the invention with The increase of array element quantity and improve.

Claims (4)

1. the low complex degree arrival direction estimation method under conformal circle battle array, which comprises the steps of:
(1) the global rotation transformation for realizing array elements polarization direction figure is rotated using Euler, solves the more of conformal array antenna Polarization problem, to construct the array data model under conformal round battle array；
(2) signal subspace of array received signal is obtained based on PASTd method；
(3) according to the design feature of spectral function, four-dimensional MUSIC spectrum peak search is down to two-dimentional MUSIC spectrum peak search, is realized conformal Low complex degree arrival direction estimation under circle battle array.
2. the low complex degree arrival direction estimation method under conformal round battle array as described in claim 1, which is characterized in that step (1) Specifically:
The steering vector of conformal antenna is codetermined by incoming signal parameter (θ, φ, γ, η), wherein γ, η are incoming signal Polarization parameter, θ, φ are pitch angle and the azimuth of incoming signal, one are made of M identical omnidirectional arrays uniform Circle battle array, direction matrix are as follows:
Since the definition and design of general array element directional diagram are all using local local coordinate system as reference, it is therefore desirable to utilize Europe Rotation is drawn to realize the global rotation transformation of array element polarization direction figure, i.e., by local array element directional diagramBe converted to global array element Directional diagram gmThe shift step of (θ, φ), each array element are as follows:
(11) unit vector in global coordinate system at (θ, φ) is subjected to rectangular co-ordinate expression:
X=sin θ cos φ, y=sin θ sin φ, z=cos θ
(12) by the local rectangular coordinates of global rectangular coordinates transformation to array element and local pole seat is obtained using Euler's rotation transformation Corresponding orientation in markRotation transformation Eulerian angles corresponding with array structure and Euler's rotational transformation matrix define respectively Are as follows:
Dm=2 (m-1) π/M, Em=0, Fm=0
(13) it is responded by the local polar coordinates of array elementObtain its expression under local rectangular coordinate system:
In formula,It indicates, and exists for the polarization of m-th of array element directional diagram under local coordinate system Following relationship:
(14) it is indicated by the local rectangular coordinate system of array element directional diagram and Euler rotates inverse transformation and obtains the complete of array element directional diagram Office's rectangular co-ordinate indicates:
(15) the array element directional diagram under global rectangular co-ordinate is finally converted into global polar coordinate representation, obtains gmθ,gmφ:
gmθ(θm,φm)=- gmZ/sinθ
gmφ(θm,φm)=- gmXsinφ+gmYcosφ
Therefore, the receipt signal model of array are as follows:
In formula,To receive data vector,For incoming signal vector；For array noise arrow Amount.
3. the low complex degree arrival direction estimation method under conformal round battle array as described in claim 1, which is characterized in that step (2) Specifically:
(21) initial value λ appropriate is selectedn(0), (0) W；
(22) to each t=1,2 ..., J (J is number of snapshots), so that x1(t)=X (t)；
(23) following variable: array received number is updated respectively to each n=1,2 ..., N (N is information source number) Characteristic valueFeature vector And array received data xn+1(t)=xn(t)-Wn(t)yn(t)；
(24) after the n=N in step (23), so that t=t+1, calculates since step (22) again；PASTd algorithm is last One step passes through xn(t) n-th of characteristic vector W of C (t) is subtractedn(t) reach algorithm deflation.
4. the low complex degree arrival direction estimation method under conformal round battle array as described in claim 1, which is characterized in that step (3) Specifically:
According to the rudimentary knowledge of array signal processing, defining array manifold spectral function is
It will be in above formulaIt is rewritten into
It enablesp(γi,ηi)=[p (γ1,η1) … p(γM,ηM)]T, then spectral function It can be write as
It enablesEasily card Q (θ, φ) is positive semidefinite matrix, and if only if (θ, φ)=(θi, φi), when i=1,2 ..., N, Q (θ, φ) is singular matrix, i.e. Q (θ, φ) is unusual at the true incident direction of information source, at this time There is det (Q (θ to matrix Q (θ, φ)i,φi))=0, i=1 ..., N, it can thus be concluded that the DOA of conformal circle battle array estimates spectral function
Carrying out two-dimensional search using above formula can be obtained the DOA information of incoming signal.
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Application publication date: 20190111