CN103383452B - Distributive array target angle-of-arrival estimation method - Google Patents

Abstract

The invention discloses a kind of distributive array target angle-of-arrival estimation method, in fact existing: according to array received data estimation array covariance matrix, by feature decomposition, to obtain signal subspace and noise subspace; Target is obtained without fuzzy angle rough estimate with ESPRIT algorithm; Computation distribution formula array pattern main lobe and the first graing lobe minimum spacing; According to this minimum spacing combining target rough estimate determination region of search, this interval only comprises the major lobe of directional diagram and does not comprise graing lobe, and the spatial spectrum in this interval, without pseudo-peak, achieves ambiguity solution; In the region of search, obtain target with MUSIC algorithm estimate without fuzzy essence.The present invention mainly solves the problem that prior art target angle-of-arrival estimation precision is low, calculated amount is large.Region of search length of the present invention is the minimum spacing of main lobe and the first graing lobe, and hunting zone is little, compares classical MUSIC algorithm and reduces calculated amount; And it is high to compare two yardstick ESPRIT algorithm angle measurement accuracy.

Description

Distributive array target angle-of-arrival estimation method

Technical field

The invention belongs to Radar Signal Processing Technology field, relate to Mutual coupling (DirectionOfArrival, DOA), specifically for the distributive array be made up of two identical arrays, a kind of distributive array target angle-of-arrival estimation method is proposed, for radar target tracking.

Background technology

In order to improve radar array angle measurement accuracy, need to expand radar array aperture, radar array aperture is larger, and radar array DOA estimated accuracy is higher.The method in expansion radar array aperture has multiple, comprises increase array number, non-homogeneously to structure the formation, and uses radar distributive array.Increase array number and can significantly improve DOA estimated accuracy, but hardware cost and calculated amount can be increased simultaneously; And radar distributive array is a kind of special thinned array, it is made up of several small-bore arrays, and the spacing of small-bore array is much larger than half-wavelength.Interfere battle array relative to early stage Microwave synthesize, radar distributive array substantially increases array freedom, and application ultra-resolution method can improve DOA estimation effect significantly.Although radar distributive array can utilize minority array element to realize the object of aperture expansion, because its base length is greater than half-wavelength, there is graing lobe in compound direction figure, there will be direction finding fuzzy.For this defect of radar distributive array, target is being detected and in tracing process, is needing to separate the DOA estimation that the fuzzy ability of direction finding accurately obtains target.

Radar distributive array ambiguity solution method comprises two-scale method, multiple signal classification (MUltipleSIgnalClassification, MUSIC) method and beam-forming schemes.Two yardstick class methods need to obtain two kinds of estimations, and a kind of is that precision is low but without fuzzy estimation, and another kind is that precision is high but have fuzzy estimation, fuzzy with what estimate without fuzzy low Accuracy extimate solution high precision.KTWong proposes the two dimension rotation invariant subspace (EstimationofSignalParametersviaRotationalInvarianceTechn iques, ESPRIT) method based on this thought and gives the condition of correct ambiguity solution.Zhu Wei etc. estimate (AmplitudeandPhaseEstimation mutually for the two yardstick width of radar distributive array, APES) method carries out DOA estimation, ambiguity solution thinking is identical with two yardstick ESPRIT method, in " interfering the blind DOA of battle array to estimate with interfere type APES algorithm realization " one, author the article pointed out that the method is that a kind of blind DOA estimates, do not rely on signal model and the DOA estimation effect more excellent than two yardstick ESPRIT method can be obtained under the condition of single snap, but pointing out that the method calculated amount is much larger than ultra-resolution method calculated amount simultaneously.Volodymyr proposition MUSIC method and beam-forming schemes solution radar distributive array fuzzy on the basis of two yardstick ESPRIT method, its essence is one group of angle estimation formula having fuzzy angle value to bring MUSIC method and Wave beam forming into ESPRIT method being obtained thus realizes ambiguity solution.Compare two yardstick ESPRIT method, the method only needs a yardstick, do not relate to the pairing that rough estimate and essence are estimated, and calculated amount is little, but due to the pseudo-peak of spatial spectrum may be higher than the peak value of real angle, therefore can not ensure the correctness of ambiguity solution completely.

Most methods mentioned above by ESPRIT method for radar distributive array estimating target DOA, because MUSIC method is higher than ESPRIT method precision, in order to improve angle measurement accuracy, there is scholar to propose to carry out DOA estimation by MUSIC method to distributive array, but still need to solve direction finding fuzzy problem.When carrying out target DOA estimation to radar distributive array by classical MUSIC method, spatial spectrum not only occurs at actual angle place that peak value but also the impact due to graing lobe there will be pseudo-peak, owing to not having other prior imformations, cannot realize ambiguity solution.For the many-valued fuzziness problem of classical MUSIC method, take charge of big building and propose peak value relative method, think that real MUSIC composes peak often higher than the pseudo-peak of MUSIC, but MUSIC peak value does not represent the size of power, and pseudo-peak may higher than true peaks under low signal-to-noise ratio, be therefore more difficultly committed to engineer applied; Jin Hubing etc. propose invariant position method, and the peak that namely array of different structure is real is constant, and the position at pseudo-peak changes, but need change array structure to take multiple measurements, and calculated amount is large, not easily realizes in actual operation.

Comprehensive above-mentioned several method can improve angle measurement accuracy under the background of radar distributive array as mentioned above, but algorithm calculated amount is large, poor real, more difficult being committed in engineer applied, reality not easily realize and angle measurement accuracy still awaits further raising.

Summary of the invention

The object of the invention is to the deficiency overcoming above-mentioned prior art, for radar distributive array, propose a kind of radar distributive array target angle-of-arrival estimation method that precision is high, efficiency is high, in real-time detection and tracking, reduce calculated amount, eliminate the impact at pseudo-peak, improve angle measurement accuracy.

For achieving the above object, present invention employs and reduce the region of search and then obtain the technical scheme of target without fuzzy essence estimation: array partition is carried out to radar distributive array and obtains target without fuzzy rough estimate, in conjunction with the minimum spacing determination region of search of the radar distributive array major lobe of directional diagram and the first graing lobe, obtain target by the spatial spectrum in the region of search to estimate without fuzzy essence, this essence is estimated to be the target angle-of-arrival estimation obtained with radar distributive array.The present invention is directed to the situation of single target, specifically comprise the steps:

Step 1, from radar distributed array receiver extracting data echoed signal X (i), is estimated the covariance matrix of radar distributive array by extracted echoed signal wherein, for 2M × 2M rank matrix, M is the submatrix array number of radar distributive array, L is fast umber of beats, and " H " represents conjugate transpose, and X (i) is array received data vector, i=1,2 ..., L, feature decomposition is carried out to this covariance matrix, obtains the expression-form of this covariance matrix about signal subspace and noise subspace: because for single target, obtain the signal subspace on rank, 2M × 1 respectively with the noise subspace on 2M × (2M-1) rank Ω _sfor the diagonal matrix of eigenvalue of maximum composition, Ω _nfor the diagonal matrix that all the other eigenwerts form.

Step 2 pair radar distributive array carries out array partition, divided two array ESPRIT algorithms is obtained to the angle rough estimate of target: the selection matrix J of structure selection two arrays ₁and J ₂, wherein J ₁=[I _{2 (M-1) × 2 (M-1)}0 _{2 (M-1) × 1}], J ₂=[0 _{2 (M-1) × 1}i _{2 (M-1) × 2 (M-1)}], then use selection matrix J ₁and J ₂structure rough estimate matrix Ψ:

Ψ＝(J ₁E _S) ⁺J ₂E _S＝((J ₁E _S) ^HJ ₁E _S) ^-1(J ₁E _S) ^HJ ₂E _S

Wherein, "+" represents that Moore-Penrose is inverse, and "-1 " representing matrix is inverted, and I is unit battle array, E in reality _swith replace, carry out feature decomposition to Ψ, if the eigenwert of Ψ is μ, then target is without fuzzy rough estimate wherein, d is radar distributive array submatrix array element distance, and λ is signal wavelength, and phase angle is got in arg () expression.

Step 3 is pointed to according to given radar beam and is synthesized radar distributive array travel direction figure, in the directional diagram that different radar beam points to, the minimum spacing obtaining radar distributive array main lobe and the first graing lobe is λ/D, and wherein D is the phase center spacing of radar distributive array two submatrixs.

Step 4 counts reference with the rough estimate of target, in conjunction with the minimum spacing of radar distributive array main lobe and the first graing lobe, forms the sweep limit G of radar beam:

$G=\left[\begin{array}{cc}{\widehat{\mathrm{\θ}}}_c-\frac{1}{2l}& {\widehat{\mathrm{\θ}}}_c+\frac{1}{2l}\end{array}\right]$

Wherein l=D/ λ, this region of search is centered by rough estimate, the length of the region of search is 1/l radian, G is the region of search of MUSIC spectrum peak search algorithm about target, because the region of search make use of the information of angle rough estimate, making target be arranged in the region of search, can ensure when searching for search target; The length of the region of search is determined by the minimum spacing of main lobe and the first graing lobe simultaneously, make the region of search not comprise fuzzy angle, thus achieve ambiguity solution, and hunting zone is little, substantially reduce the calculated amount of spectrum peak search.

Step 5 obtains target without fuzzy smart estimated result, specifically in region of search G, carry out spectrum peak search with MUSIC algorithm, make scanning beam point to different orientation and obtain the spatial spectrum of MUSIC algorithm in region of search G, any graing lobe is not comprised because the region of search only comprises main lobe, then the MUSIC spatial spectrum of this region of search does not have pseudo-peak to occur, namely achieve ambiguity solution, according to the Power estimation formula of MUSIC algorithm, target is estimated without fuzzy essence for:

$\widehat{\mathrm{\θ}}=\arg \underset{\mathrm{\θ}\∈G}{\max }\frac{1}{a^H\left(\mathrm{\θ}\right){\hat{E}}_N{\hat{E}}_N^{H}a\left(\mathrm{\θ}\right)}$

Wherein, a (θ) is radar distributive array steering vector, for the estimation of noise subspace.This essence is estimated to be the target angle-of-arrival estimation obtained with radar distributive array.

The present invention is directed to the DOA estimation problem of radar distributive array, have employed and reduce the interval scheme obtaining target and estimate without fuzzy essence of MUSIC algorithm search: first, receive data estimation array covariance matrix according to radar array, by feature decomposition, obtain signal subspace and noise subspace; Secondly, target is obtained without fuzzy angle rough estimate based on ESPRIT algorithm by extracted radar target signal; Reference is counted again with rough estimate, the minimum spacing of main lobe and the first graing lobe is calculated according to radar distributive array compound direction figure, determine the region of search of target, this region of search only comprises the main lobe of the compound direction figure pointing to target direction and does not comprise graing lobe, spatial spectrum does not have pseudo-peak to occur, achieves ambiguity solution; Finally obtain target at region of search MUSIC spectrum peak search algorithm to estimate without fuzzy angle essence, this essence is estimated to be the target angle-of-arrival estimation obtained with radar distributive array.

Realization of the present invention is also: the process obtaining target rough estimate based on ESPRIT algorithm of step 2 comprises the steps:

(1) radar distributive array is suitable for the array partition obtaining estimating without Fuzzy Rough:

If radar distributive array is made up of two submatrixs, two submatrixs are the even linear array that array number is M, the adjacent array element distance of submatrix is d (d≤0.5 λ), λ is signal wavelength, the array that front M-1 array element of front M-1 array element of the 1st submatrix and the 2nd submatrix is formed is designated as a gust A, the array that rear M-1 array element of rear M-1 array element of the 1st submatrix and the 2nd submatrix is formed is designated as a gust B, and what battle array A and battle array B was division can obtain two arrays that target estimates without Fuzzy Rough;

(2) target is obtained without fuzzy rough estimate to divided array ESPRIT algorithm:

The translation invariant relation of battle array A and battle array B can represent with following formula:

$\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right)J_{1}a\left(\mathrm{\θ}\right)=J_{2}a\left(\mathrm{\θ}\right)$

Wherein, J ₁=[I _{2 (M-1) × 2 (M-1)}0 _{2 (M-1) × 1}], J ₂=[0 _{2 (M-1) × 1}i _{2 (M-1) × 2 (M-1)}], J ₁and J ₂be the selection matrix selecting array, wherein, J ₁for selecting the selection matrix of battle array A, J ₂for selecting the selection matrix of battle array B.I is unit battle array, for radar distributive array steering vector, $a_1\left(\mathrm{\θ}\right)={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right),\·\·\·,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}(M-1)d\sin \left(\mathrm{\θ}\right)\right)]}^T,$ $B={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}D\sin \left(\mathrm{\θ}\right)\right)]}^T;$ Order $\mathrm{\Φ}=\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right),$ Then have:

J ₁a(θ)Φ＝J ₂a(θ)

And have J according to Estimation of Spatial Spectrum theory ₁e _sΨ=J ₂e _s, Ψ=T ^-1Φ T, further, translation invariant relation can be represented by following formula:

Ψ＝(J ₁E _S)+J ₂E _S＝((J ₁E _S) ^HJ ₁E _S) ^-1(J ₁E _S) ^HJ ₂E _S

Wherein, Ψ is rough estimate matrix, () ⁺represent that Moore-Penrose is inverse, "-1 " representing matrix is inverted, actual when solving, E _swith replace.Feature decomposition is carried out to Ψ, if the eigenwert of Ψ is μ, due to Ψ=T ^-1the eigenwert of Φ T, Ψ is the element of diagonal matrix Φ principal diagonal, obtains the angle rough estimate of target accordingly this estimated accuracy is lower but without fuzzy, wherein phase angle is got in arg () expression.

The present invention constructs by carrying out array partition to radar distributive array the array that two have translation invariance, obtains target without fuzzy rough estimate to constructed two array ESPRIT algorithms.

Realization of the present invention is also: the calculating radar distributive array major lobe of directional diagram of step 3 and the concrete steps of the first graing lobe minimum spacing comprise:

Radar beam is made to point to θ ₀, the radar distributive array directional diagram expression formula of synthesis is:

$Y\left(\mathrm{\θ}\right)=2\left|\cos \left(\mathrm{\π}\frac{D}{\mathrm{\λ}}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)\frac{\sin \left(\frac{\mathrm{\π}}{2}M(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}{\sin \left(\frac{\mathrm{\π}}{2}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}\right|$

Wherein, M is submatrix array number, and D is the phase center spacing of two submatrixs, and λ is wavelength, and main lobe is positioned at θ ₀place, the position of the first graing lobe is θ ₀two neighbouring maximum point θ ₁=arcsin (θ ₀-λ/D), θ ₂=arcsin (θ ₀+ λ/D); The distance of the first graing lobe of main lobe and its both sides is respectively L ₁=θ ₀-arcsin (θ ₀-λ/D), L ₂=arcsin (θ ₀+ λ/D)-θ ₀, when radar beam points to change, different radar beams points to corresponding different radar distributive array directional diagrams, works as θ ₀when=0, L ₁, L ₂reach minimum, now L ₁=L ₂=arcsin (λ/D) ≈ λ/D, namely the radar distributive array major lobe of directional diagram and the first graing lobe minimum spacing are λ/D.

The present invention is when carrying out radar distributive array target angle-of-arrival estimation, utilize rough estimate captured target, the basis of rough estimate is counted with rough estimate the central point of the region of search, with the length that the minimum spacing of radar distributive array main lobe and the first graing lobe is the region of search, the region of search determined like this guarantees to obtain target and estimates without fuzzy essence, and hunting zone is little, calculated amount is reduced greatly.

The present invention compared with prior art has the following advantages:

(1) when carrying out DOA estimation with classical MUSIC algorithm to distributive array, need to carry out spectrum peak search in whole angular field of view, hunting zone is large, cause algorithm calculated amount very large, and spatial spectrum exists pseudo-peak, accurately cannot obtain target DOA estimation; And the present invention make use of the information of angle rough estimate when determining the region of search, centered by rough estimate, in the neighborhood of rough estimate, determining the region of search, making target be arranged in the region of search, can ensure when searching for search target; The length of the region of search is determined by the minimum spacing of main lobe and the first graing lobe simultaneously, make the region of search not comprise fuzzy angle, thus achieve ambiguity solution, and region of search scope is little, substantially reduce the calculated amount of spectrum peak search.

(2) in existing most of radar distributive array DOA estimation method, essence estimation ESPRIT algorithm obtains, and the DOA estimated accuracy of ESPRIT algorithm needs to improve further; The present invention is with composing MUSIC algorithm estimating target arrival bearing, and because MUSIC arithmetic accuracy is higher than ESPRIT arithmetic accuracy, the inventive method performance is better than two yardstick ESPRIT algorithm.

Accompanying drawing explanation

Fig. 1 is the realization flow figure of the inventive method;

Fig. 2 is the inventive method radar distributive array schematic diagram used;

Fig. 3 is radar distributive array directional diagram and subarray patterns;

Fig. 4 is the space spectrogram that DOA estimates, wherein, and the target angle of arrival space spectrogram that Fig. 4 (a) is classical MUSIC algorithm, the target angle of arrival space spectrogram that Fig. 4 (b) is the inventive method;

Fig. 5 is the curve map of the inventive method and two yardstick ESPRIT algorithm signal-noise ratio threshold;

Fig. 6 is that the inventive method DOA estimates that root-mean-square error is with the change curve of submatrix phase center spacing with the ratio of wavelength under different signal to noise ratio (S/N ratio).

Embodiment

Content of the present invention and effect is described in detail below in conjunction with accompanying drawing.

Embodiment 1

Radar distributive array is generally made up of two or more independent array pulled open, radar distributive array of the present invention is made up of two arrays, the receiver of these arrays receives echoed signal simultaneously, carry out coherent synthesized estimation to parameter to receiving data, compared with conventional arrays, distributive array defines large aperture array when identical array number, and the method is the method in array extending aperture conventional in practical engineering application.

With reference to Fig. 1, the present invention is a kind of distributive array target angle-of-arrival estimation method, and for distributive array exploitation, the estimation of the target angle of arrival comprises the steps:

Step 1: extract echoed signal from the radar receiver of each antenna of radar distributive array, L sampling is carried out to echoed signal, the sampling of these target echo signals constitutes array received data vector, utilizes the X (i) that samples for L time of array received data vector to estimate array covariance matrix wherein i=1,2 ..., L is right carry out feature decomposition, obtain signal subspace and noise subspace

Fig. 2 is the present invention's radar distributive array schematic diagram used, array of the present invention is D by two phase center spacing and identical even linear array is formed, even linear array array number is M and adjacent array element distance is d (d≤0.5 λ), λ is signal wavelength, and each array element is desirable isotropy array element.

Suppose have a far field narrow band signal (target) to incide array, complex envelope, incident angle are respectively s (t), θ, with Fig. 2 neutron array 1 Far Left array element for reference, then radar distributed array receiver data vector is such as formula shown in (1).

X(t)＝a(θ)s(t)+n(t)(1)

$a\left(\mathrm{\θ}\right)=B\⊗a_1\left(\mathrm{\θ}\right)---\left(2\right)$

$a_1\left(\mathrm{\θ}\right)={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right),\·\·\·,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}(M-1)d\sin \left(\mathrm{\θ}\right)\right)]}^T---\left(3\right)$

$B={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}D\sin \left(\mathrm{\θ}\right)\right)]}^T---\left(4\right)$

In formula (1) ~ formula (4), t=1,2 ... L, L are fast umber of beats, and n (t) is for tieing up noise vector in 2M × 1, and noise is average is 0, variance is σ ²additive white Gaussian noise, noise mutual statistical in each array element is independent, and independent with signal.A (θ) is radar distributive array steering vector, a ₁(θ) be the steering vector of submatrix 1, " T " represents transposition, represent that Kronecker amasss, s (t) is signal phasor.

According to array received data estimation array covariance matrix right carry out Eigenvalues Decomposition, obtain expression-form about signal subspace and noise subspace:

$\hat{R}=\frac{1}{L}\underset{j=1}{\overset{L}{\mathrm{\Σ}}}X\left(i\right)X^H\left(i\right)={\hat{E}}_S{\mathrm{\Ω}}_S{\hat{E}}_S^H+{\hat{E}}_N{\mathrm{\Ω}}_N{\hat{E}}_N^H---\left(5\right)$

the eigenvalue of maximum characteristic of correspondence vector space of opening be signal subspace all the other eigenwert characteristic of correspondence vectors space of opening be noise subspace Ω _sfor the diagonal matrix of eigenvalue of maximum composition, Ω _nfor the diagonal matrix that all the other eigenwerts form, " H " represents conjugate transpose.

Step 2: carry out array partition to radar distributive array, namely constructs the array that two have translation invariant relation, obtains target without fuzzy rough estimate to these two arrayed applications ESPRIT algorithms of structure according to radar distributed array receiver data vector.

Observe the radar distributive array shown in Fig. 2, there is long and short two class baseline in it: the spacing d of the adjacent array element of submatrix is Short baseline, and two submatrix phase center space D are Long baselines.ESPRIT algorithm obtains without fuzzy estimation based on Short baseline d, and because base length is short, what obtain is the estimation that precision is low, is referred to as rough estimate.For the radar distributive array of Fig. 2, first, carry out the array partition being suitable for obtaining estimating without Fuzzy Rough, the figure neutron array 1 i.e. even linear array of radar distributive array, front M-1 array element of its front M-1 array element and submatrix 2 is divided into new array, the new array formed is designated as a gust A, rear M-1 array element of submatrix 1 and rear M-1 array element of submatrix 2 form new array and are designated as a gust B, battle array A and battle array B is two arrays dividing and obtain, this division ensure that gust A and battle array B has translation invariance, utilizes these two arrays can obtain without fuzzy angle on target rough estimate.Then, obtain target for battle array A and battle array B application ESPRIT algorithm and estimate without fuzzy essence, the translation invariant relation of battle array A and battle array B can be used represent.Wherein, J ₁=[I _{2 (M-1) × 2 (M-1)}0 _{2 (M-1) × 1}], J ₂=[0 _{2 (M-1) × 1}i _{2 (M-1) × 2 (M-1)}], J ₁and J ₂be selection matrix, J ₁for selecting the selection matrix of battle array A, J ₂for selecting the selection matrix of battle array B, I is unit battle array, and a (θ) is radar distributive array steering vector.Order j is had according to Estimation of Spatial Spectrum theory ₁e _sΨ=J ₂e _s, Ψ=T ^-1Φ T, tries to achieve Ψ=(J ₁e _s) ⁺j ₂e _s=((J ₁e _s) ^hj ₁e _s) ^-1(J ₁e _s) ^hj ₂e _s, Ψ is rough estimate matrix, actual E when solving _swith replace, wherein, () ⁺represent that Moore-Penrose is inverse, "-1 " representing matrix is inverted, and T is nonsingular matrix.Feature decomposition is carried out to Ψ, if the eigenwert of Ψ is μ, due to Ψ=T ^-1Φ T, then the eigenwert of Ψ is the element of diagonal matrix Φ principal diagonal, obtains angle on target rough estimate by the expression formula of Φ

${\widehat{\mathrm{\θ}}}_c=\arcsin (\arg \left(\mathrm{\μ}\right)/(2\mathrm{\πd}/\mathrm{\λ}))---\left(6\right)$

Wherein, arg () represents and gets phase angle, and this angle estimation value precision is lower but without fuzzy, and this angle estimation value is the center of the region of search of the present invention.

Step 3: according to controlling antenna wave beam to point, radar distributive array travel direction figure is synthesized, to different antennae beam position, calculate the distance of corresponding main lobe and the first graing lobe, and then obtain the minimum spacing of the radar distributive array major lobe of directional diagram and the first graing lobe.

For the radar distributive array of Fig. 2, obtaining controlling antenna wave beam to point by formula (2) ~ formula (4) is θ ₀the expression formula of radar distributive array directional diagram:

$Y\left(\mathrm{\θ}\right)=2\left|\cos \left(\mathrm{\π}\frac{D}{\mathrm{\λ}}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)\frac{\sin \left(\frac{\mathrm{\π}}{2}M(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}{\sin \left(\frac{\mathrm{\π}}{2}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}\right|---\left(7\right)$

Main lobe is at θ ₀place, two the first graing lobes are main lobe θ ₀the maximum point of both sides, its amplitude is closest to the amplitude of main lobe, and the position of two the first graing lobes is respectively θ ₁=arcsin (θ ₀-λ/D), θ ₂=arcsin (θ ₀+ λ/D), the spacing of main lobe and two the first graing lobes is respectively L ₁=θ ₀-arcsin (θ ₀-λ/D), L ₂=arcsin (θ ₀+ λ/D)-θ ₀.Easily know: work as θ ₀when=0, L ₁, L ₂reach minimum, now L ₁=L ₂=arcsin (λ/D).Due to for radar distributive array, D is much larger than λ, and the minimum spacing of main lobe and the first graing lobe is approximately λ/D, and this minimum spacing is the length of the region of search of the present invention centered by rough estimate.Fig. 3 is the directional diagram of radar distributive array and submatrix 1 in Fig. 2, wherein, controlling antenna wave beam to point 0 degree, the even linear array of submatrix to be adjacent array element distance be half-wavelength, submatrix array number M is 8, two submatrix phase center space D is that 20 λ, Fig. 3 neutron array main lobe is wide, distributive array main lobe is narrow, and submatrix main lobe width is approximately 9 times of distributive array main lobe width.

Step 4: count reference with the rough estimate of target, namely obtains target without fuzzy rough estimate from step 2, in conjunction with the minimum spacing of radar distributive array main lobe and the first graing lobe, forms radar beam sweep limit, namely determines the region of search of MUSIC algorithm about target.

When DOA estimation is carried out with classical MUSIC algorithm to radar distributive array, because compound direction figure exists graing lobe, there is pseudo-peak at graing lobe place in MUSIC spatial spectrum, calculates ratio juris according to MUSIC, now owing to there is no other prior imformations, directly accurately target DOA estimation cannot be obtained.In order to eliminate the impact at pseudo-peak, the present invention reduces the region of search, the region of search is made only to comprise the main lobe of the compound direction figure pointing to this target direction and not comprise graing lobe, because pseudo-peak occurs at graing lobe place, when carrying out DOA at this region of search spectrum MUSIC algorithm and estimating, spatial spectrum does not have pseudo-peak and occurs.

Make l=D/ λ, the rough estimate of target obtained by formula (6), consider the error of rough estimate, then the region of search of this target is this region of search is centered by rough estimate, and burst length is 1/l radian, and when spectrum peak search is carried out in this interval, the region of search does not comprise any graing lobe and comprises main lobe, and spatial spectrum there will not be pseudo-peak and guarantees to search target.

Step 5: in the fixed region of search, spectrum peak search is carried out to radar distributive array MUSIC algorithm, be formed in the space spectrogram of radar distributive array within the scope of the region of search, calculate ratio juris according to MUSIC and obtain target in conjunction with the space spectrogram of radar distributive array and estimate without fuzzy essence.

Determine the region of search, with MUSIC algorithm, spectrum peak search is carried out, because the region of search does not comprise graing lobe to this target in corresponding region of search G, spatial spectrum occurs without pseudo-peak, meanwhile, comprise target rough estimate owing to searching plain interval, therefore can obtain without fuzzy estimation.The present invention estimates about the essence of target wherein, a (θ) is radar distributive array steering vector, for the estimation of noise subspace.This essence is estimated to be the target angle-of-arrival estimation obtained with radar distributive array.

When DOA estimation being carried out to distributive array with classical MUSIC algorithm, need to carry out spectrum peak search in whole angular field of view, hunting zone causes greatly algorithm calculated amount very large, have impact on the response of radar real-time working, speed and efficiency, and spatial spectrum exists pseudo-peak, accurately target DOA estimation cannot be obtained.When DOA estimation being carried out to distributive array by the inventive method, owing to have selected the suitable region of search before spectrum peak search, compared to classical MUSIC algorithm, the scope of the region of search is little, reduce calculated amount, and ambiguity solution is achieved while reduction calculated amount, and can the estimating target angle of arrival rapidly, make radar can carry out real-time detection and tracking to target.

Effect of the present invention is further illustrated by following simulation result:

In following all emulation, suppose that submatrix 1 as shown in Figure 2 and submatrix 2 are the even linear array that adjacent array element distance is half-wavelength, and submatrix array element number M is 8, the present invention is all applicable to the signal wavelength lambda meeting far field narrow band signal condition.

Embodiment 2

Distributive array target angle-of-arrival estimation method is with embodiment 1.

Emulation 1: the space spectrogram of classical MUSIC algorithm and the inventive method contrasts;

Simulated conditions a: target incides radar distributive array with 30 °, fast umber of beats L is 100, and signal to noise ratio (S/N ratio) is 5dB, and radar distributive array submatrix phase center space D is 50 λ, and step-size in search is 0.01 °, and Monte-Carlo experiment number is 100 times.

Simulation result: the space spectrogram of classical MUSIC algorithm is as shown in Fig. 4 (a), and the space spectrogram of the inventive method is as shown in 4 (b).As shown in Figure 4: the spatial spectrum of classical MUSIC algorithm has multiple extreme point to exist, except true peaks, there is multiple pseudo-peak in spatial spectrum, true peaks is the central peak of spatial spectrum in Fig. 4 (a), there is multiple pseudo-peak in central peak both sides, owing to not having prior imformation, the appearance at a large amount of pseudo-peak can lead to errors estimation, accurately cannot estimate target DOA according to MUSIC algorithm principle by spatial spectrum; And the present invention is owing to have selected the suitable region of search, there is not pseudo-peak in the spatial spectrum formed in the region of search under 100 Monte-Carlo experiments, see Fig. 4 (b), only there is a peak value, because rough estimate guarantees to search target, the angle that this peak value is corresponding is target angle-of-arrival estimation, and peak value is concentrated and appeared at 30 ° of places, illustrates and present invention achieves correct ambiguity solution and angle measurement accuracy is high.The present invention is directed in distributive array target angle-of-arrival estimation method, eliminate the impact at the pseudo-peak that graing lobe causes, achieve ambiguity solution, accurately obtain target DOA estimation, and region of search scope is little, substantially reduce the calculated amount of spectrum peak search.

Embodiment 3

Distributive array target angle-of-arrival estimation method is with embodiment 1.

Emulation 2: the inventive method contrasts with the curve map of two yardstick ESPRIT algorithm signal-noise ratio threshold;

First the root-mean-square error defining DOA estimation is θ is the real angle value of target arrival bearing, for the angle essence estimated value of target arrival bearing.

Simulated conditions a: target incides radar distributive array with 30 °, fast umber of beats L is 100, and submatrix phase center space D is 20 λ, and step-size in search is 0.01 °, and Monte-Carlo experiment number is 500 times.

Simulation result: the relation curve of the inventive method and two yardstick ESPRIT algorithm root-mean-square error and signal to noise ratio (S/N ratio) as shown in Figure 5.As shown in Figure 5: along with the increase of signal to noise ratio (S/N ratio), the root-mean-square error of two kinds of algorithms reduces gradually, and under low signal-to-noise ratio, the root-mean-square error of the inventive method is significantly less than the root-mean-square error of two yardstick ESPRIT algorithm, this is because two kinds of algorithms utilize same rough estimate, and the estimated accuracy of the inventive method is higher than the estimated accuracy of two yardstick ESPRIT algorithm.

Embodiment 4

Distributive array target angle-of-arrival estimation method is with embodiment 1.

Emulation 3: under different signal to noise ratio (S/N ratio), the inventive method DOA estimates the change of root-mean-square error with submatrix phase center spacing.

Simulated conditions a: target incides radar distributive array from 30 °, fast umber of beats L is 100, submatrix phase center space D be 10 λ to 100 λ, step-size in search is 0.01 °, and Monte-Carlo experiment number is 500 times.

The angle measurement root-mean-square error that simulation result: Fig. 6 provides the inventive method when signal to noise ratio (S/N ratio) is respectively 0dB, 3dB is with the change curve of submatrix phase center spacing and wavelength ratio.As shown in Figure 6: root-mean-square error first reduces rear increase with the increase of submatrix phase center spacing and wavelength ratio, namely there is a fuzzy thresholding, when signal to noise ratio (S/N ratio) is 0dB, fuzzy thresholding is 40 λ, and when signal to noise ratio (S/N ratio) is 3dB, fuzzy thresholding is 60 λ.When signal to noise ratio (S/N ratio) is 0dB, the submatrix phase center spacing range being applicable to the work of radar distributive array is that 20 λ are to 40 λ, can provide without the fuzzy and angle estimation value that precision is high at this active section radar distributive array, when submatrix phase center spacing is more than 40 λ, the angle estimation result that radar distributive array provides is poor, and radar distributive array is not operated in this scope; When signal to noise ratio (S/N ratio) is 3dB, the submatrix phase center spacing range being applicable to the work of radar distributive array is that 20 λ are to 60 λ, equally, can provide without the fuzzy and angle estimation value that precision is high at this active section radar distributive array, when submatrix phase center spacing is more than 60 λ, the angle estimation result that radar distributive array provides is poor, and radar distributive array is not operated in this scope; And signal to noise ratio (S/N ratio) is higher, the submatrix phase center spacing range being applicable to the work of radar distributive array is larger.Present invention utilizes the region of performance the best in curve, participate in the estimation of the radar distributive array target angle of arrival.

Radar distributive array target angle-of-arrival estimation method of the present invention, mainly solves the problem that prior art target angle-of-arrival estimation precision is low, calculated amount is large.By distributed array receiver data estimation distributive array covariance matrix, by feature decomposition, obtain signal subspace and noise subspace; Target is obtained without fuzzy angle rough estimate with ESPRIT algorithm; The minimum spacing of Computation distribution formula array pattern main lobe and the first graing lobe; According to the minimum spacing of main lobe and the first graing lobe, the rough estimate of combining target, determines the region of search; In the region of search, obtain target with MUSIC algorithm estimate without fuzzy essence.The present invention will compose MUSIC algorithm application arrived in distributive array target angle-of-arrival estimation by reducing hunting zone, compare two yardstick ESPRIT algorithm and will improve angle measurement accuracy, compare classical MUSIC algorithm and reduce calculated amount.

Claims (3)

1. a distributive array target angle-of-arrival estimation method, is characterized in that, described target angle-of-arrival estimation method comprises the following steps:

Step 1, from radar distributed array receiver extracting data echoed signal X (i), is estimated the covariance matrix of radar distributive array by extracted echoed signal wherein, for 2M × 2M rank matrix, M is the submatrix array number of radar distributive array, and L is fast umber of beats, and " H " represents conjugate transpose, and X (i) is array received data vector, i=1,2 ..., L; Feature decomposition is carried out to this covariance matrix, obtains the expression-form of this covariance matrix about signal subspace and noise subspace: setting only has a target, obtains the signal subspace on rank, 2M × 1 respectively with the noise subspace on 2M × (2M-1) rank Ω _sfor the diagonal matrix of eigenvalue of maximum composition, Ω _nfor the diagonal matrix that all the other eigenwerts form;

Step 2 pair radar distributive array carries out array partition, carries out angle rough estimate to divided two array ESPRIT algorithms to target: the selection matrix J of structure selection two arrays ₁=[I _{2 (M-1) × 2 (M-1)}o _{2 (M-1) × 1}], J ₂=[O _{2 (M-1) × 1}i _{2 (M-1) × 2 (M-1)}], wherein O _{2 (M-1) × 1}representation dimension is the full 0 matrix of 2 (M-1) × 1, then uses selection matrix J ₁and J ₂structure rough estimate matrix Ψ:

Ψ＝(J ₁E _S) ⁺J ₂E _S＝((J ₁E _S) ^HJ ₁E _S) ^-1(J ₁E _S) ^HJ ₂E _S

Wherein, "+" represents that Moore-Penrose is inverse, and "-1 " representing matrix is inverted, and I is unit battle array, E in reality _swith replace, carry out feature decomposition to Ψ, if the eigenwert of Ψ is μ, then target is without fuzzy rough estimate wherein, d is the submatrix array element distance of radar distributive array, and λ is signal wavelength, and phase angle is got in arg () expression;

Step 3 is pointed to according to radar beam and is synthesized radar distributive array travel direction figure, in the directional diagram that different radar beam points to, be λ/D by calculating the minimum spacing of the radar distributive array major lobe of directional diagram and the first graing lobe, wherein D is the phase center spacing of two submatrixs of radar distributive array;

Step 4 counts reference with target without fuzzy rough estimate, in conjunction with the minimum spacing of the radar distributive array major lobe of directional diagram and the first graing lobe, forms the sweep limit G of radar beam:

$G=\left[\begin{array}{cc}{\widehat{\mathrm{\θ}}}_c-\frac{1}{2l}& {\widehat{\mathrm{\θ}}}_c+\frac{1}{2l}\end{array}\right]$

Wherein l=D/ λ, this region of search is centered by rough estimate, and the length of the region of search is 1/l, G is the region of search of MUSIC spectrum peak search algorithm about target;

Step 5 obtains target and estimates without fuzzy essence: in region of search G, carry out spectrum peak search with MUSIC algorithm, make scanning beam point to different orientation and obtain the spatial spectrum of MUSIC algorithm in region of search G, according to the Power estimation formula of MUSIC algorithm, target is estimated without fuzzy essence for:

$\widehat{\mathrm{\θ}}=\arg \underset{\mathrm{\θ}\∈G}{\max }\frac{1}{a^H\left(\mathrm{\θ}\right){\hat{E}}_N{\hat{E}}_N^{H}a\left(\mathrm{\θ}\right)}$

Wherein, a (θ) is radar distributive array steering vector, for the estimation of noise subspace, this essence is estimated to be the target angle-of-arrival estimation obtained with radar distributive array.

2. distributive array target angle-of-arrival estimation method according to claim 1, is characterized in that, carrying out angle rough estimate with ESPRIT algorithm to target and comprise the steps: described in step 2

2.1 pairs of radar distributive arrays are suitable for obtaining the array partition without Fuzzy Rough estimation:

If radar distributive array is made up of two submatrixs, two submatrixs are the even linear array that array number is M, the adjacent array element distance of submatrix is d, d≤0.5 λ, λ is signal wavelength, the division array that front M-1 array element of front M-1 array element of the 1st submatrix and the 2nd submatrix is formed is designated as a gust A, and the division array that rear M-1 array element of rear M-1 array element of the 1st submatrix and the 2nd submatrix is formed is designated as a gust B;

2.2 pairs of array ESPRIT algorithms divided obtain target without fuzzy rough estimate:

The translation invariant relation following formula of battle array A and battle array B represents:

$\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right)J_{1}a\left(\mathrm{\θ}\right)=J_{2}a\left(\mathrm{\θ}\right)$

Wherein, J ₁=[I _{2 (M-1) × 2 (M-1)}o _{2 (M-1) × 1}], J ₂=[O _{2 (M-1) × 1}i _{2 (M-1) × 2 (M-1)}], J ₁and J ₂for selecting the selection matrix of two arrays and battle array A and battle array B, I is unit battle array, for radar distributive array steering vector, $a_1\left(\mathrm{\θ}\right)={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right),...,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}(M-1)d\sin \left(\mathrm{\θ}\right)\right)]}^T,$ $B={[1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}D\sin \left(\mathrm{\θ}\right)\right)]}^T;$ Order $\mathrm{\Φ}=\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\λ}}d\sin \left(\mathrm{\θ}\right)\right),$ Then have:

J ₁a(θ)Φ＝J ₂a(θ)

And have J according to Estimation of Spatial Spectrum theory ₁e _sΨ=J ₂e _s, Ψ=T ^-1Φ T, wherein T is nonsingular matrix, and further, translation invariant relation is expressed from the next:

Ψ＝(J ₁E _S) ⁺J ₂E _S＝((J ₁E _S) ^HJ ₁E _S) ^-1(J ₁E _S) ^HJ ₂E _S

Wherein, Ψ is rough estimate matrix, () ⁺represent that Moore-Penrose is inverse, "-1 " representing matrix is inverted, actual when solving, E _swith replace; Feature decomposition is carried out to Ψ, if the eigenwert of Ψ is μ, due to Ψ=T ^-1the eigenwert of Φ T, Ψ is the element of diagonal matrix Φ principal diagonal, obtains the angle rough estimate of target accordingly wherein arg () represents and gets phase angle, and this estimated accuracy is lower but without fuzzy.

3. distributive array target angle-of-arrival estimation method according to claim 1, is characterized in that, the calculating radar distributive array major lobe of directional diagram described in step 3 and the concrete steps of the first graing lobe minimum spacing comprise:

When radar beam is oriented to θ ₀time, the radar distributive array directional diagram expression formula of synthesis is:

$Y\left(\mathrm{\θ}\right)=2\left|\cos \left(\mathrm{\π}\frac{D}{\mathrm{\λ}}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)\frac{\sin \left(\frac{\mathrm{\π}}{2}M(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}{\sin \left(\frac{\mathrm{\π}}{2}(\sin \mathrm{\θ}-\sin {\mathrm{\θ}}_0)\right)}\right|$

Wherein, M is radar distributive array submatrix array number, and D is the phase center spacing of two submatrixs of radar distributive array, and λ is wavelength, and D is much larger than λ, and main lobe is at θ ₀place, two the first graing lobes are main lobe θ ₀the maximum point of both sides, its amplitude is closest to the amplitude of main lobe, and the position of two the first graing lobes is respectively θ ₁=arcsin (θ ₀-λ/D), θ ₂=arcsin (θ ₀+ λ/D), the distance of the first graing lobe of main lobe and its both sides is respectively L ₁=θ ₀-arcsin (θ ₀-λ/D), L ₂=arcsin (θ ₀+ λ/D)-θ ₀, different radar beams points to corresponding different radar distributive array directional diagrams, when radar beam points to θ ₀when=0, L ₁, L ₂reach minimum, now, L ₁=L ₂=arcsin (λ/D) ≈ λ/D, namely main lobe and the first graing lobe minimum spacing are λ/D.