CN103383452A - Estimation method of target angle of arrival of distributed array - Google Patents

Abstract

The invention discloses an estimation method of a target angle of arrival of a distributed array. The estimation method includes that an array covariance matrix is estimated according to array receiving data, and a signal subspace and a noise subspace are obtained through characteristic decomposition; target unambiguous angle rough estimation is obtained through an ESPRIT algorithm; the minimum distance between a major lobe of a directional diagram of the distributed array and a first grating lobe is calculated; a search region is determined according to the minimum distance by combining target rough estimation, wherein the search region only contains the major lobe of the directional diagram and does not contain the grating lobe, the spatial spectrum of the search region does not have spurious peaks, and ambiguity resolving is achieved; target unambiguous fine estimation is obtained in the search region through a MUSIC algorithm. The estimation method mainly solves problems in the prior art of low estimation accuracy and large calculation amount of the target angle of arrival. The length of the search region is the minimum distance between the major lobe and the first grating lobe, the search range is small, and the calculation amount is reduced compared with the classic MUSIC algorithm, and the angle measurement accuracy is high compared with the dual-scale ESPRIT algorithm.

Description

Distributive array target angle of arrival method of estimation

Technical field

The invention belongs to the Radar Signal Processing Technology field, relate to direction of arrival and estimate (Direction Of Arrival, DOA), specifically for the distributive array that is consisted of by two identical arrays, propose a kind of distributive array target angle of arrival method of estimation, be used for radar target tracking.

Background technology

In order to improve the radar array angle measurement accuracy, need to enlarge the radar array aperture, the radar array aperture is larger, and radar array DOA estimated accuracy is higher.The method in expansion radar array aperture has multiple, comprises the increase array number, and non-homogeneous structuring the formation used the radar distributive array.Increase array number and can significantly improve the DOA estimated accuracy, but can increase hardware cost and calculated amount simultaneously; And the radar distributive array is a kind of special thinned array, and it is comprised of several small-bore arrays, and the spacing of small-bore array is much larger than half-wavelength.With respect to the synthetic battle array of interfering of early stage microwave, the radar distributive array has improved array freedom greatly, uses ultra-resolution method and can improve significantly the DOA estimation effect.Although the minority array element of can utilizing the radar distributive array realizes the purpose of aperture expansion, greater than half-wavelength, compound direction is strivied for survival at graing lobe due to its base length, can direction finding occur fuzzy.For this defective of radar distributive array, target is surveyed with tracing process in, need to separate the DOA that the fuzzy ability of direction finding accurately obtains target and estimate.

Radar distributive array ambiguity solution method comprises two-scale method, multiple signal classification (MUltiple SIgnal Classification, 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 fuzzy estimation is arranged, with estimate to separate the fuzzy of high precision estimation without fuzzy low precision.K T Wong has proposed two dimension rotation invariant subspaces (Estimation of Signal Parameters via Rotational Invariance Techniques, ESPRIT) method based on this thought and has provided the condition of correct ambiguity solution.Zhu Wei etc. estimate (Amplitude and Phase Estimation for the radar distributive array mutually with two yardstick width, APES) method is carried out the DOA estimation, the ambiguity solution thinking is identical with two yardstick ESPRIT methods, the author points out that the method is that a kind of blind DOA estimates in " realizing interfering the blind DOA of battle array to estimate with interfere type APES algorithm " literary composition, do not rely on signal model and can obtain under the condition of single snap than the more excellent DOA estimation effect of two yardstick ESPRIT methods, but pointing out that simultaneously the method calculated amount is much larger than the ultra-resolution method calculated amount.Volodymyr proposes to use the fuzzy of MUSIC method and beam-forming schemes solution radar distributive array on the basis of two yardstick ESPRIT methods, thereby its essence is that one group of angle estimation formula that has fuzzy angle value to bring MUSIC method and wave beam formation into that the ESPRIT method obtains is realized ambiguity solution.Compare two yardstick ESPRIT methods, 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 because spatial spectrum pseudo-peak may be higher than the peak value of true angle, therefore can not guarantee the correctness of ambiguity solution fully.

The top most methods of mentioning uses the ESPRIT method for radar distributive array estimating target DOA, because the MUSIC method is higher than ESPRIT method precision, in order to improve angle measurement accuracy, there is the scholar to propose with the MUSIC method, distributive array to be carried out DOA and estimates, but still need to solve the direction finding fuzzy problem.When the radar distributive array was carried out target DOA estimation with classical MUSIC method, spatial spectrum peak value not only occurred but also because pseudo-peak can appear in the impact of graing lobe, owing to there is no other prior imformations, can't realize ambiguity solution at the actual angle place.Many-valued fuzziness problem for classical MUSIC method, take charge of big building and propose the peak value relative method, think that real MUSIC spectrum peak is often higher than the pseudo-peak of MUSIC, but the MUSIC peak value does not represent the size of power, and under low signal-to-noise ratio, pseudo-peak may be higher than true peaks, and therefore the more difficult engineering that is committed to is used; Jin Hubing etc. propose the invariant position method, and namely the real peak of the array of different structure is constant, and the position at pseudo-peak changes, and takes multiple measurements but need to change array structure, and calculated amount is large, is difficult in actual operation realizing.

Comprehensively as mentioned above, above-mentioned several method can improve angle measurement accuracy under the background of radar distributive array, but the algorithm calculated amount is large, real-time is poor, more difficultly be committed to that engineering is used, be difficult for realizing in reality and angle measurement accuracy still awaits further raising.

Summary of the invention

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

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

Step 1 is estimated the covariance matrix of radar distributive array from radar distributed array receiver extracting data echoed signal X (i) by the echoed signal of extracting

Wherein, Be 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 the array received data vector, i=1,2 ..., L, this covariance matrix is carried out feature decomposition, obtains this covariance matrix about the expression-form of signal subspace and noise subspace:

Because for single target, obtain respectively the signal subspace on 2M * 1 rank

And the noise subspace on rank of 2M * (2M-1)

Ω _SBe the diagonal matrix that eigenvalue of maximum forms, Ω _NDiagonal matrix for all the other eigenwerts compositions.

Step 2 pair radar distributive array carries out array partition, and two arrays dividing are obtained the angle rough estimate of target with the ESPRIT algorithm: structure is selected the selection matrix J of two arrays ₁And J ₂, J wherein 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, Moore-Penrose is contrary in "+" expression, and " 1 " representing matrix is inverted, and I is unit matrix, E in reality _SWith

Replace, Ψ is carried out feature decomposition, the eigenwert of establishing Ψ is μ, and 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 radar distributive array travel direction figure synthetic according to given radar beam, in the directional diagram that different radar beams point to, the minimum spacing that obtains radar distributive array main lobe and the first graing lobe is λ/D, and wherein D is the phase center spacing of two submatrixs of radar distributive array.

Step 4 is counted 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:

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

L=D/ λ wherein, this region of search is centered by rough estimate, the length of the region of search is the 1/l radian, G is MUSIC spectrum peak search algorithm about the region of search of target, utilized the information of angle rough estimate due to the region of search, make target be arranged in the region of search, can guarantee to search target when searching for; 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, thereby realized ambiguity solution, and the hunting zone is little, has greatly reduced the calculated amount of spectrum peak search.

Step 5 is obtained target without fuzzy smart estimated result, specifically carry out spectrum peak search with the MUSIC algorithm in region of search G, make scanning beam point to different orientation and obtain the spatial spectrum of MUSIC algorithm in region of search G, because only comprising main lobe, the region of search do not comprise any graing lobe, the MUSIC spatial spectrum of this region of search does not have pseudo-peak to occur, namely realized ambiguity solution, according to the spectrum estimator 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,

Estimation for noise subspace.This essence is estimated to be with the resulting target angle of arrival of radar distributive array and is estimated.

The present invention is directed to the DOA estimation problem of radar distributive array, adopted and dwindled MUSIC algorithm search interval and obtain the scheme that target is estimated without fuzzy essence: at first, estimate the array covariance matrix according to the radar array receive data, by feature decomposition, obtain signal subspace and noise subspace; Secondly, obtain target without fuzzy angle rough estimate based on the ESPRIT algorithm by the radar target signal that extracts; Count reference with rough estimate again, calculate the minimum spacing of main lobe and the first graing lobe 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 that points to target direction and does not comprise graing lobe, spatial spectrum does not have pseudo-peak to occur, and has realized ambiguity solution; Obtain target in the region of search with MUSIC spectrum peak search algorithm at last and estimate without fuzzy angle essence, this essence is estimated to be with the resulting target angle of arrival of radar distributive array and is estimated.

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

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

If the radar distributive array is comprised 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 consists of 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 consists of is designated as a gust B, and what battle array A and battle array B were division can access two arrays that target is estimated without Fuzzy Rough;

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

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

$\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right)J_{1}a\left(\mathrm{\&theta;}\right)=J_{2}a\left(\mathrm{\&theta;}\right)$

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 of 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 matrix,

Be radar distributive array steering vector, $a_1\left(\mathrm{\&theta;}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right),\&CenterDot;\&CenterDot;\&CenterDot;,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(M-1)d\sin \left(\mathrm{\&theta;}\right)\right)]}^T,$ $B={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}D\sin \left(\mathrm{\&theta;}\right)\right)]}^T;$ Order $\mathrm{\&Phi;}=\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right),$ Have:

J ₁a(θ)Φ＝J ₂a(θ)

And according to the Estimation of Spatial Spectrum theory, J is arranged ₁E _sΨ=J ₂E _s, Ψ=T ^-1Φ T, further, the 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 the rough estimate matrix, () ⁺Moore-Penrose is contrary in expression, and " 1 " representing matrix is inverted, during actual finding the solution, and E _SWith

Replace.Ψ is carried out feature decomposition, and the eigenwert of establishing Ψ is μ, due to Ψ=T ^-1Φ T, the eigenwert of Ψ is the element of diagonal matrix Φ principal diagonal, obtains accordingly the angle rough estimate of target

This estimated accuracy is lower but without fuzzy, wherein phase angle is got in arg () expression.

The present invention obtains target without fuzzy rough estimate to two arrays of constructing with the ESPRIT algorithm by the radar distributive array being carried out two arrays with translation invariance of array partition structure.

Realization of the present invention also is: 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:

Make radar beam point to θ ₀, synthetic radar distributive array directional diagram expression formula is:

$Y\left(\mathrm{\&theta;}\right)=2\left|\cos \left(\mathrm{\&pi;}\frac{D}{\mathrm{\&lambda;}}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)\frac{\sin \left(\frac{\mathrm{\&pi;}}{2}M(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)}{\sin \left(\frac{\mathrm{\&pi;}}{2}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)}\right|$

Wherein, M is the submatrix array number, and D is the phase center spacing of two submatrixs, and λ is wavelength, and main lobe is positioned at θ ₀The place, the position of the first graing lobe is θ ₀Near two 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 pointed to variation, different radar beams pointed to corresponding different radar distributive array directional diagrams, works as θ ₀=0 o'clock, L ₁, L ₂Reach minimum, at this moment L ₁=L ₂(the ≈ λ/D of λ/D), namely the radar distributive array major lobe of directional diagram and the first graing lobe minimum spacing are λ/D to=arcsin.

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

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

(1) with classical MUSIC algorithm, distributive array is carried out DOA when estimating, need to carry out spectrum peak search in whole angular field of view, the hunting zone is large, causes the algorithm calculated amount very large, and there is pseudo-peak in spatial spectrum, can't accurately obtain target DOA estimation; And the present invention has utilized the information of angle rough estimate when determining the region of search, centered by rough estimate, determines the region of search in the neighborhood of rough estimate, makes target be arranged in the region of search, can guarantee to search target when searching for; 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, thereby realized ambiguity solution, and region of search scope is little, has greatly reduced the calculated amount of spectrum peak search.

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

Description of drawings

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

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

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)s.

Embodiment

Describe content of the present invention and effect in detail below in conjunction with accompanying drawing.

Embodiment 1

The radar distributive array generally is made of two or more independent array that pull open, radar distributive array of the present invention is made of two arrays, the receiver of these arrays receives echoed signal simultaneously, receive data is carried out the synthetic estimation of completing parameter of coherent, compare with conventional arrays, distributive array has been in the situation that identical array number has formed the large aperture array, and the method is the method in array extending commonly used in practical engineering application aperture.

With reference to Fig. 1, the present invention is a kind of distributive array target angle of arrival method of estimation, and for the 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, echoed signal is carried out L sampling, the sampling of these target echo signals has formed the array received data vector, utilizes L the sampling X (i) of array received data vector to estimate the array covariance matrix

I=1 wherein, 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 that D and identical even linear array consist of by two phase center spacings, the even linear array array number is that M and adjacent array element distance are d (d≤0.5 λ), λ is signal wavelength, and each array element is desirable isotropy array element.

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

X(t)＝a(θ)s(t)+n(t) (1)

$a\left(\mathrm{\&theta;}\right)=B\&CircleTimes;a_1\left(\mathrm{\&theta;}\right)---\left(2\right)$

$a_1\left(\mathrm{\&theta;}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right),\&CenterDot;\&CenterDot;\&CenterDot;,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(M-1)d\sin \left(\mathrm{\&theta;}\right)\right)]}^T---\left(3\right)$

$B={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000921442900012.png,HSA00000921442900042.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}D\sin \left(\mathrm{\&theta;}\right)\right)]}^T---\left(4\right)$

In formula (1)～formula (4), t=1,2 ... L, L are fast umber of beats, and n (t) is 2M * 1 dimension noise vector, and noise is that average is 0, variance is σ ²Additive white Gaussian noise, noise mutual statistical on 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, Expression Kronecker is long-pending, and 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:

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

The eigenvalue of maximum characteristic of correspondence vector space of opening be signal subspace

All the other eigenwert characteristic of correspondence vectors spaces of opening be noise subspace Ω _SBe the diagonal matrix that eigenvalue of maximum forms, Ω _NBe the diagonal matrix that all the other eigenwerts form, " H " represents conjugate transpose.

Step 2: the radar distributive array is carried out array partition, namely construct two arrays with translation invariant relation, these two arrayed applications ESPRIT algorithms of constructing are obtained target without fuzzy rough estimate according to radar distributed array receiver data vector.

Observe radar distributive array shown in Figure 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 baseline.The ESPRIT algorithm obtains without fuzzy estimation based on short baseline d, and because base length is short, what obtain is the low estimation of precision, is referred to as rough estimate.Radar distributive array for Fig. 2, at first, be suitable for obtaining the array partition estimated without Fuzzy Rough, figure neutron array 1 is the 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 that consists of is designated as a gust A, rear M-1 array element of rear M-1 array element of submatrix 1 and submatrix 2 consists of new array and is designated as a gust B, battle array A and battle array B are and divide two arrays that obtain, this division has guaranteed that battle array A and battle array B have translation invariance, utilize these two arrays can access without fuzzy angle on target rough estimate.Then, obtain target without fuzzy essence estimation for battle array A and battle array B application ESPRIT algorithm, the translation invariant relation of battle array A and battle array B can be used

Expression.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 matrix, and a (θ) is radar distributive array steering vector.Order

According to the Estimation of Spatial Spectrum theory, J is arranged 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 the rough estimate matrix, E during actual finding the solution _SWith

Replace, wherein, () ⁺Moore-Penrose is contrary in expression, and " 1 " representing matrix is inverted, and T is nonsingular matrix.Ψ is carried out feature decomposition, and the eigenwert of establishing Ψ is μ, due to Ψ=T ^-1Φ T, the eigenwert of Ψ is the element of diagonal matrix Φ principal diagonal, obtains the angle on target rough estimate by the expression formula of Φ

${\widehat{\mathrm{\&theta;}}}_c=\arcsin (\arg \left(\mathrm{\&mu;}\right)/(2\mathrm{\&pi;d}/\mathrm{\&lambda;}))---\left(6\right)$

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

Step 3: synthetic to radar distributive array travel direction figure according to controlling antenna wave beam to point, to the 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:

$Y\left(\mathrm{\&theta;}\right)=2\left|\cos \left(\mathrm{\&pi;}\frac{D}{\mathrm{\&lambda;}}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)\frac{\sin \left(\frac{\mathrm{\&pi;}}{2}M(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)}{\sin \left(\frac{\mathrm{\&pi;}}{2}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)}\right|---\left(7\right)$

Main lobe is at θ ₀The place, two the first graing lobes are main lobe θ ₀The maximum point of both sides, its amplitude are near 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 ₀Easily know: work as θ ₀=0 o'clock, L ₁, L ₂Reach minimum, at this moment L ₁=L ₂=arcsin (λ/D).Due to for the 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, submatrix is that adjacent array element distance is the even linear array of half-wavelength, submatrix array number M is that 8, two submatrix phase center space D are 20 λ, and Fig. 3 neutron array main lobe is wide, the distributive array main lobe is narrow, and the submatrix main lobe width is approximately 9 times of the distributive array main lobe width.

Step 4: the rough estimate with target is counted reference, 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 the radar beam sweep limit, determines that namely the MUSIC algorithm is about the region of search of target.

When the radar distributive array is carried out the DOA estimation with classical MUSIC algorithm, because compound direction is strivied for survival at graing lobe, the MUSIC spatial spectrum pseudo-peak occurs at the graing lobe place, according to the principle of MUSIC algorithm, can't directly accurately obtain target DOA estimation owing to there is no other prior imformations this moment.In order to eliminate the impact at pseudo-peak, the present invention dwindles the region of search, the main lobe of the compound direction figure that makes the region of search only comprise to point to this target direction and do not comprise graing lobe, because pseudo-peak occurs at the graing lobe place, when when this region of search is carried out the DOA estimation with spectrum MUSIC algorithm, 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, the region of search of this target is

This region of search is centered by rough estimate, and burst length is the 1/l radian, and when carrying out spectrum peak search in this interval, the region of search does not comprise any graing lobe and comprises main lobe, and spatial spectrum pseudo-peak can not occur and guarantee to search target.

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

Determine the region of search, this target has been carried out spectrum peak search with the MUSIC algorithm in corresponding region of search G, because the region of search does not comprise graing lobe, spatial spectrum occurs without pseudo-peak, simultaneously, comprise the 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,

Estimation for noise subspace.This essence is estimated to be with the resulting target angle of arrival of radar distributive array and is estimated.

When with classical MUSIC algorithm, distributive array being carried out the DOA estimation, need to carry out spectrum peak search in whole angular field of view, the hunting zone causes greatly the algorithm calculated amount very large, response, speed and the efficient of radar real-time working have been affected, and there is pseudo-peak in spatial spectrum, can't accurately obtain target DOA estimation.When with the inventive method, distributive array being carried out the DOA estimation, owing to having selected the suitable region of search before spectrum peak search, than classical MUSIC algorithm, the scope of the region of search is little, reduced calculated amount, and realized ambiguity solution when reducing calculated amount, the estimating target angle of arrival, make radar to carry out real-time detection and tracking to target rapidly.

Effect of the present invention further illustrates by following simulation result:

In following all emulation, suppose that as shown in Figure 2 submatrix 1 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 that satisfies far field narrow band signal condition.

Embodiment 2

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

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

Simulated conditions: a target incides the radar distributive array with 30 °, and 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 the 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 a plurality of extreme points to exist, except true peaks, there are a plurality of pseudo-peaks in spatial spectrum, true peaks is the central peak of spatial spectrum in Fig. 4 (a), there are a plurality of pseudo-peaks in the central peak both sides, owing to there is no prior imformation, the appearance at a large amount of pseudo-peaks estimation that can lead to errors can't accurately estimate target DOA according to the MUSIC algorithm principle by spatial spectrum; And the present invention is owing to having selected the suitable region of search, there is not pseudo-peak in the spatial spectrum that forms in the region of search under 100 Monte-Carlo experiments, referring to Fig. 4 (b), a peak value is only arranged, because rough estimate guarantees to search target, the angle that this peak value is corresponding is the target angle of arrival to be estimated, and peak value concentrates and appear at 30 ° and locate, illustrate the present invention realized correct ambiguity solution and angle measurement accuracy high.The present invention is directed in distributive array target angle of arrival method of estimation, eliminated the impact at the pseudo-peak that graing lobe causes, realized ambiguity solution, accurately obtain target DOA estimation, and region of search scope is little, greatly reduced the calculated amount of spectrum peak search.

Embodiment 3

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

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

At first the root-mean-square error that defines the DOA estimation is

θ is target arrival bearing's true angle value,

Angle essence estimated value for the target arrival bearing.

Simulated conditions: a target incides the radar distributive array with 30 °, and 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 the 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 algorithms, this is because of two kinds of rough estimates that the algorithm utilization is same, and the estimated accuracy of the inventive method is higher than the estimated accuracy of two yardstick ESPRIT algorithms.

Embodiment 4

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

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

Simulated conditions: target incides the radar distributive array from 30 °, and 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 °, the Monte-Carlo experiment number is 500 times.

When simulation result: Fig. 6 provides signal to noise ratio (S/N ratio) and is respectively 0dB, 3dB, the angle measurement root-mean-square error of the inventive method 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 has a fuzzy thresholding, signal to noise ratio (S/N ratio) when being 0dB fuzzy thresholding be 40 λ, signal to noise ratio (S/N ratio) when being 3dB fuzzy thresholding be 60 λ.When signal to noise ratio (S/N ratio) is 0dB, the submatrix phase center spacing range that is fit to the work of radar distributive array is that 20 λ are to 40 λ, can provide without angle estimation value fuzzy and that precision is high at this active section radar distributive array, when submatrix phase center spacing surpasses 40 λ, the angle estimation result that the radar distributive array provides is poor, and the radar distributive array has not been operated in this scope; When signal to noise ratio (S/N ratio) is 3dB, the submatrix phase center spacing range that is fit to the work of radar distributive array is that 20 λ are to 60 λ, equally, can provide without angle estimation value fuzzy and that precision is high at this active section radar distributive array, when submatrix phase center spacing surpasses 60 λ, the angle estimation result that the radar distributive array provides is poor, and the radar distributive array has not been operated in this scope; And signal to noise ratio (S/N ratio) is higher, and the submatrix phase center spacing range that is fit to the work of radar distributive array is larger.The present invention has utilized the zone of curve performance the best, participates in the estimation of the radar distributive array target angle of arrival.

Radar distributive array target angle of arrival method of estimation of the present invention mainly solves the problem that prior art target angle of arrival estimated accuracy 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; Obtain target without fuzzy angle rough estimate with the 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 region of search is determined in the rough estimate of combining target; Obtaining target with the MUSIC algorithm in the region of search estimates without fuzzy essence.The present invention will compose the MUSIC algorithm application and arrive during the distributive array target angle of arrival estimates by dwindling the hunting zone, compare two yardstick ESPRIT algorithms and improve angle measurement accuracy, compare classical MUSIC algorithm and reduce calculated amount.

Claims (3)

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

Step 1 is estimated the covariance matrix of radar distributive array from radar distributed array receiver extracting data echoed signal X (i) by the echoed signal of extracting

Wherein, Be 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 the array received data vector, i=1, and 2 ..., L; This covariance matrix is carried out feature decomposition, obtains this covariance matrix about the expression-form of signal subspace and noise subspace:

Setting only has a target, obtains respectively the signal subspace on 2M * 1 rank

And the noise subspace on rank of 2M * (2M-1)

Ω _SBe the diagonal matrix that eigenvalue of maximum forms, Ω _NDiagonal matrix for all the other eigenwerts compositions;

Step 2 pair radar distributive array carries out array partition, and two arrays dividing are carried out the angle rough estimate with the ESPRIT algorithm to target: structure is selected the selection matrix J of two arrays 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, Moore-Penrose is contrary in "+" expression, and " 1 " representing matrix is inverted, and I is unit matrix, E in reality _SWith

Replace, Ψ is carried out feature decomposition, the eigenwert of establishing Ψ is μ, and 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 radar distributive array travel direction figure synthetic according to radar beam, in the directional diagram that different radar beams point to, be λ/D by the minimum spacing that calculates 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 is counted 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:

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

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

Step 5 is obtained target and is estimated without fuzzy essence: carry out spectrum peak search with the MUSIC algorithm in region of search G, make scanning beam point to different orientation and obtain the spatial spectrum of MUSIC algorithm in region of search G, according to the spectrum estimator of MUSIC algorithm, target is estimated without fuzzy essence For:

$\widehat{\mathrm{\&theta;}}=\arg \underset{\mathrm{\&theta;}\&Element;G}{\max }\frac{1}{a^H\left(\mathrm{\&theta;}\right){\hat{E}}_N{\hat{E}}_N^{H}a\left(\mathrm{\&theta;}\right)}$

Wherein, a (θ) is radar distributive array steering vector,

Be the estimation of noise subspace, this essence is estimated to be with the resulting target angle of arrival of radar distributive array and is estimated.

2. distributive array target angle of arrival method of estimation according to claim 1, is characterized in that, the described process that obtains the target rough estimate based on the ESPRIT algorithm of step 2 comprises the steps:

2.1 the radar distributive array is suitable for obtaining the array partition estimated without Fuzzy Rough:

If the radar distributive array is comprised 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 consists of 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 consists of is designated as a gust B;

2.2 the array divided is obtained target without fuzzy rough estimate with the ESPRIT algorithm:

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

$\exp \left(j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right)J_{1}a\left(\mathrm{\&theta;}\right)=J_{2}a\left(\mathrm{\&theta;}\right)$

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 ₂For selecting the selection matrix of two arrays, I is unit matrix,

Be radar distributive array steering vector, $a_1\left(\mathrm{\&theta;}\right){[1,\exp \left(2\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right),\&CenterDot;\&CenterDot;\&CenterDot;,\exp \left(2\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(M-1)d\sin \left(\mathrm{\&theta;}\right)\right)]}^T,$ $B={[1,\exp \left(j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}D\sin \left(\mathrm{\&theta;}\right)\right)]}^T;$ Order $\mathrm{\&Phi;}=\exp \left(j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}d\sin \left(\mathrm{\&theta;}\right)\right),$ Have:

J ₁a(θ)Φ＝J ₂a(θ)

And according to the Estimation of Spatial Spectrum theory, J is arranged ₁E _sΨ=J ₂E _s, Ψ=T ^-1Φ T, further, the translation invariant relation is 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 the rough estimate matrix, () ⁺Moore-Penrose is contrary in expression, and " 1 " representing matrix is inverted, during actual finding the solution, and E _SWith Replace; Ψ is carried out feature decomposition, and the eigenwert of establishing Ψ is μ, due to Ψ=T ^-1Φ T, the eigenwert of Ψ is the element of diagonal matrix Φ principal diagonal, obtains accordingly the angle rough estimate of target

Wherein phase angle is got in arg () expression, and this estimated accuracy is lower but without fuzzy.

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

When radar beam is oriented to θ ₀The time, synthetic radar distributive array directional diagram expression formula is:

$Y\left(\mathrm{\&theta;}\right)=2\left|\cos \left(\mathrm{\&pi;}\frac{D}{\mathrm{\&lambda;}}(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)\frac{\sin \left(\frac{\mathrm{\&pi;}}{2}M(\sin \mathrm{\&theta;}-\sin {\mathrm{\&theta;}}_0)\right)}{\sin \left(\frac{\mathrm{\&pi;}}{2}(\sin \mathrm{\&theta;}-{\sin \mathrm{\&theta;}}_0)\right)}\right|$

Wherein, M is radar distributive array submatrix array number, and D is radar distributive array submatrix phase center spacing, and λ is wavelength, and D is much larger than λ, and main lobe is at θ ₀The place, two the first graing lobes are main lobe θ ₀The maximum point of both sides, its amplitude are near 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 ₀=0 o'clock, L ₁, L ₂Reach minimum, at this moment, L ₁=L ₂(the ≈ λ/D of λ/D), namely main lobe and the first graing lobe minimum spacing are λ/D to=arcsin.

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