CN105629206B - The sane space-time Beamforming Method of airborne radar and system under steering vector mismatch - Google Patents

The sane space-time Beamforming Method of airborne radar and system under steering vector mismatch Download PDF

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CN105629206B
CN105629206B CN201610122010.1A CN201610122010A CN105629206B CN 105629206 B CN105629206 B CN 105629206B CN 201610122010 A CN201610122010 A CN 201610122010A CN 105629206 B CN105629206 B CN 105629206B
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steering vector
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space
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CN105629206A (en
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黄磊
李强
张基宏
张沛昌
廖斌
赵博
周汉飞
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Shenzhen University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/2813—Means providing a modification of the radiation pattern for cancelling noise, clutter or interfering signals, e.g. side lobe suppression, side lobe blanking, null-steering arrays

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  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention provides the sane space-time Beamforming Method of the airborne radar under steering vector mismatch and system, method to include：The angle of arrival of the flying height of airborne platform, speed and target echo signal is initialized, and determines the Doppler frequency of radar echo signal；The receipt signal model of array antenna is established, and spatial-temporal integration covariance matrix is built according to the estimate of radar echo signal angle of arrival and Doppler frequency；According to spatial-temporal integration covariance matrix, clutter plus noise subspace is determined；The object function and constraints of steering vector estimator are established, and is solved according to SDP Relaxation method to obtain the actual steering vector of target echo signal；According to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.The present invention can obtain the optimal estimation value of expectation target steering vector, make Beam-former in success clutter reduction and only form wave beam in expectation target direction, avoid amplifying noise power, so as to expand the output Signal to Interference plus Noise Ratio of Beam-former.

Description

The sane space-time Beamforming Method of airborne radar and system under steering vector mismatch
Technical field
The present invention relates to the airborne radar under array antenna and airborne radar technical field, more particularly to steering vector mismatch Sane space-time Beamforming Method and system.
Background technology
The main task of airborne radar is to identify under the background environment of complexity and track expectation target, therefore, it is necessary to Null is formed at land clutter, wave beam is formed at target.Due to the motion of carrier aircraft platform, the ground-clutter spectrum of airborne phased array radar Main clutter broadening is shown in Doppler frequency domain the characteristics of.In addition, there is coupling in the ground-clutter spectrum in spatial domain and time-domain Conjunction relation.Traditional time domain or spatial filter can not form the recess to match with land clutter.Space-time adaptive processing (Space-Time Adaptive Processing, STAP) technology can suppress land clutter from spatial domain, time domain two dimension joint, make Obtain it and be widely applied to airborne radar in Ground moving target detection.STAP has the room and time free degree, energy simultaneously It is enough to form recess on spatial spectrum and Doppler frequency domain spectrum plane, effectively suppress land clutter, while strengthen target signal direction The gain at place.However, when the incident angle and Doppler-frequency estimation of radar echo signal have deviation, STAP output letter Miscellaneous noise ratio (signal-to-clutter-plus-noise ratio, SCNR) performance is by degradation.
In view of the above-mentioned problems, currently used robust adaptive beamforming method has based on uncertain collection constraint and is based on Amplitude response constrained procedure.Thought based on uncertain collection constraint is by scholar institutes such as Vorobyov S A and Gershman A B It is proposed.Thought of such algorithm based on modular constraint with uncertain collection constraint, and utilize the realization pair of worst best performance criterion The maximum improvement of beamforming algorithm performance.Robust ada- ptive beamformer algorithm based on uncertain collection constraint class needs to know that expectation is led To the parameter such as the norm border of vector error or the symmetric positive definite matrix related to the error, these parameters directly affect ripple The performance of beamformer.And in practice, these parameters are not easy accurately to try to achieve.Thought based on amplitude response constraint is by Yu Z What the scholars such as L and Er M H put forward.Robust ada- ptive beamformer algorithm based on amplitude response constraint is wide due to adding main beam Degree, the noise for constraining angular interval will be received greatly, and disturb the probability close to main beam also to become big, so as to cause output letter dry Make an uproar reduces than (signal-to-interference-plus-noise ratio, SINR).
Robust ada- ptive beamformer algorithm based on uncertain collection constraint class needs to know the norm side for it is expected steering vector error The parameter such as boundary or the symmetric positive definite matrix related to the error, these parameters directly affect the performance of Beam-former.And In practice, these parameters are not easy accurately to try to achieve.Robust ada- ptive beamformer algorithm based on amplitude response constraint is due to adding master Beam angle, the noise for constraining angular interval will be received greatly, and disturb the probability close to main beam also to become big, defeated so as to cause Go out SINR reductions.
Therefore, prior art could be improved and develop.
The content of the invention
In view of in place of above-mentioned the deficiencies in the prior art, it is an object of the invention to provide the airborne thunder under steering vector mismatch Up to sane space-time Beamforming Method and system, it is intended to solve in the prior art when the incident angle and Duo Pu of radar echo signal When Le Frequency Estimation has deviation, the problem of miscellaneous noise ratio performance is by degradation is believed in STAP output.
In order to achieve the above object, this invention takes following technical scheme：
A kind of airborne radar sane space-time Beamforming Method under steering vector mismatch, wherein, methods described include with Lower step：
A, the angle of arrival of the flying height of initialization airborne platform, speed and target echo signal, and determine radar return The Doppler frequency of signal；
B, the receipt signal model of array antenna is established, and estimating according to radar echo signal angle of arrival and Doppler frequency Evaluation builds spatial-temporal integration covariance matrix；
C, according to spatial-temporal integration covariance matrix, clutter plus noise subspace is determined；
D, the object function and constraints of steering vector estimator are established, and solves to obtain according to SDP Relaxation method The actual steering vector of target echo signal；
E, according to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.
The sane space-time Beamforming Method of airborne radar under the steering vector mismatch, wherein, the step B is specifically wrapped Include：
B1, establish array antenna received signals model x (t)=ast(θ0,fd0)s(t)+ncn(t)；Wherein, s (t) is expectation The echo-signal of target, ast(θ0,fd0) it is space-time steering vector, ncn(t) space white noise is added for land clutter signal；
The space angle section that B2, note echo-signal angle of arrival are located at is Θ, and Doppler frequency section is F, Then building spatial-temporal integration covariance matrix according to the estimate of radar echo signal angle of arrival and Doppler frequency is
The sane space-time Beamforming Method of airborne radar under the steering vector mismatch, wherein, the step C is specifically wrapped Include：
C1, it is to spatial-temporal integration covariance matrixEigenvalues Decomposition is carried out to obtain To signal subspace E；Wherein E=[e1 e2 … eP], eiIt is the main characteristic vector corresponding to i-th of dominant eigenvalue, i value Scope is [1,2, P], and i is integer, and P is the number of dominant eigenvalue；
C2, according to signal subspace E, obtain its orthogonal complement spaceAndWherein, ast0For expectation target The actual steering vector of echo-signal,For clutter plus noise subspace.
The sane space-time Beamforming Method of airborne radar under the steering vector mismatch, wherein, the step D is specifically wrapped Include：
D1, according to the power output after Beam-former clutter reduction and noiseAnd maximize the phase Output power signal criterion is hoped, the object function and constraints for determining steering vector estimator are：
WhereinFor F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M launches for each bay Pulse number,K is the sampling snap number to echo-signal；
D2, solved according to SDP Relaxation method to obtain the actual steering vector of target echo signal
The sane space-time Beamforming Method of airborne radar under the steering vector mismatch, wherein, basis in the step EDraw the weight coefficient of array antenna
A kind of airborne radar sane space-time Beam Forming System under steering vector mismatch, wherein, including：
Initialization module, for initializing the flying height of airborne platform, speed and the angle of arrival of target echo signal, and Determine the Doppler frequency of radar echo signal；
Matrix builds module, for establishing the receipt signal model of array antenna, and according to radar echo signal angle of arrival Spatial-temporal integration covariance matrix is built with the estimate of Doppler frequency；
Subspace acquisition module, for according to spatial-temporal integration covariance matrix, determining clutter plus noise subspace；
Steering vector acquisition module, for establishing the object function and constraints of steering vector estimator, and according to half Set pattern draws method of relaxation and solves to obtain the actual steering vector of target echo signal；
Weight coefficient acquisition module, for according to the undistorted method of minimum variance, obtaining the weight coefficient of array antenna.
The sane space-time Beam Forming System of airborne radar under the steering vector mismatch, wherein, the matrix builds mould Block specifically includes：
Model establishes unit, for establishing array antenna received signals model x (t)=ast(θ0,fd0)s(t)+ncn(t)； Wherein, s (t) be expectation target echo-signal, ast(θ0,fd0) it is space-time steering vector, ncn(t) sky is added for land clutter signal Between white noise；
Matrix acquiring unit, for being Θ when the space angle section that is located at of note echo-signal angle of arrival, Doppler frequency Section is F, then building spatial-temporal integration covariance matrix according to the estimate of radar echo signal angle of arrival and Doppler frequency is
The sane space-time Beam Forming System of airborne radar under the steering vector mismatch, wherein, the subspace obtains Module specifically includes：
Resolving cell.For being to spatial-temporal integration covariance matrixCarry out special Value indicative decomposes to obtain signal subspace E；Wherein E=[e1 e2 … eP], eiMain feature corresponding to i-th of dominant eigenvalue to Amount, i span is [1,2, P], and i is integer, and P is the number of dominant eigenvalue；
Orthogonal cells, for according to signal subspace E, obtaining its orthogonal complement spaceAndWherein, ast0 It is expected the actual steering vector of target echo signal,For clutter plus noise subspace.
The sane space-time Beam Forming System of airborne radar under the steering vector mismatch, wherein, the steering vector obtains Modulus block specifically includes：
Steering vector estimator acquiring unit, for according to the power output after Beam-former clutter reduction and noiseAnd desired signal power output criterion is maximized, determine the object function peace treaty of steering vector estimator Beam condition is：
WhereinFor F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M launches for each bay Pulse number,K is the sampling snap number to echo-signal；
Actual steering vector solves unit, for being solved to obtain the reality of target echo signal according to SDP Relaxation method Steering vector
The sane space-time Beam Forming System of airborne radar under the steering vector mismatch, wherein, the weight coefficient obtains Basis in modulus blockDraw the weight coefficient of array antenna
The sane space-time Beamforming Method of airborne radar and system under steering vector mismatch of the present invention, method bag Include：The angle of arrival of the flying height of airborne platform, speed and target echo signal is initialized, and determines the more of radar echo signal General Le frequency；Establish the receipt signal model of array antenna, and estimating according to radar echo signal angle of arrival and Doppler frequency Evaluation builds spatial-temporal integration covariance matrix；According to spatial-temporal integration covariance matrix, clutter plus noise subspace is determined；Foundation is led To the object function and constraints of vector estimator, and solved according to SDP Relaxation method to obtain the reality of target echo signal Border steering vector；According to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.The present invention can obtain expectation mesh Mark the optimal estimation value of steering vector so that Beam-former is on the premise of success clutter reduction, only in expectation target direction Wave beam is formed, avoids the amplification to noise power, so as to further expand the output Signal to Interference plus Noise Ratio of Beam-former.
Brief description of the drawings
Fig. 1 is the sane space-time Beamforming Method preferred embodiment of airborne radar under steering vector mismatch of the present invention Flow chart.
Fig. 2 is the sane space-time Beam Forming System preferred embodiment of airborne radar under steering vector mismatch of the present invention Structured flowchart.
Embodiment
The present invention provides the sane space-time Beamforming Method of airborne radar and system under steering vector mismatch, to make this hair Bright purpose, technical scheme and effect are clearer, clear and definite, and the embodiment that develops simultaneously referring to the drawings is to of the invention further detailed Explanation.It should be appreciated that specific embodiment described herein is not intended to limit the present invention only to explain the present invention.
Fig. 1 is refer to, it is the sane space-time Beamforming Method of airborne radar under steering vector mismatch of the present invention The flow chart of preferred embodiment.It is as shown in figure 1, described
Step S100, the angle of arrival of the flying height of initialization airborne platform, speed and target echo signal, and determine thunder Up to the Doppler frequency of echo-signal；
Step S200, the receipt signal model of array antenna is established, and according to radar echo signal angle of arrival and Doppler The estimate structure spatial-temporal integration covariance matrix of frequency；
Step S300, according to spatial-temporal integration covariance matrix, clutter plus noise subspace is determined；
Step S400, the object function and constraints of steering vector estimator are established, and according to SDP Relaxation method Solution obtains the actual steering vector of target echo signal；
Step S500, according to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.
In embodiments of the invention, first according to estimate expectation target angle of arrival (direction-of-arrival, DOA) and Doppler frequency, a spatial-temporal integration covariance matrix for including desired signal steering vector information is built.Then it is sharp With the characteristic that desired signal and clutter, noise subspace are mutually orthogonal, clutter plus noise subspace is derived, and swear as being oriented to Measure a constraints of estimator.Then using steering vector norm constraint and maximization desired signal power criterion, design A kind of optimal steering vector estimator.Quadratically constrained quadratic programming problem is converted into by linear gauge using SDP Relaxation method The problem of drawing.Finally, using the undistorted response criteria of minimum variance, sane space-time Beam-former is established, solves array antenna The weight coefficient of each array element.
Specifically, setting airborne radar works in positive side radar mode, i.e. airborne platform flight side in the step s 100 To consistent with bay plane.The pulse recurrence frequency of radar is set as fr, radar wavelength λ, distance by radar ground level For H, airborne platform flying speed is v, and the radar echo signal incidence angle of expectation target is θ0.Determine it is expected according to above parameter The Doppler frequency f of target echo signald0, and
Specifically, the step S200 is specifically included：
Step S201, array antenna received signals model x (t)=a is establishedst(θ0,fd0)s(t)+ncn(t)；Wherein, s (t) For the echo-signal of expectation target, ast(θ0,fd0) it is space-time steering vector, ncn(t) space white noise is added for land clutter signal；
Step S202, the space angle section that note echo-signal angle of arrival is located at is Θ, and Doppler frequency section is F, then Building spatial-temporal integration covariance matrix according to the estimate of radar echo signal angle of arrival and Doppler frequency is
In step s 201, using the even linear array being made up of N number of bay, adjacent array element at intervals of λ/2, each Array element launches M coherent pulse, then the reception signal x (t) of array antenna can be expressed as：
X (t)=ast(θ0,fd0)s(t)+ncn(t) (1)
Wherein, s (t) be expectation target echo-signal, ast(θ0,fd0) it is space-time steering vector, ncn(t) it is land clutter Signal adds space white noise.
ast(θ0,fd0) it is that Kronecker product is asked to the spatial domain steering vector and time domain steering vector of expectation target echo-signal (Kronecker product) is obtained, i.e.,：
Wherein, as(θ0) for it is expected target echo signal spatial domain steering vector, at(fd0) it is it is expected target echo signal Time domain steering vector,Represent Kronecker product computing.as(θ0) and at(fd0) can be expressed as respectively：
Wherein, []TThe transposition of vector or matrix is represented, d is the interval of adjacent array element.
Because in airborne radar real work, the echo-signal angle of arrival and Doppler frequency of estimation inevitably go out Existing deviation.It is now assumed that the space angle section that echo-signal angle of arrival is located at is Θ, Doppler frequency section is F, then builds one Individual spatial-temporal integration covariance matrix
In formula (2), ()HRepresent the conjugate transposition of vector or matrix.The spatial-temporal integration covariance matrix includes mesh Mark the steering vector information of echo-signal.
When deviation be present in the estimate of radar echo signal angle of arrival and Doppler frequency, ast(θ0,fd0) further table It is shown asWherein,The estimate of the angle of arrival of deviation to be present,Deviation to be present Doppler-frequency estimation value, δ are the steering vector error of estimation.It is convenient for expression, hereafter by ast(θ0,fd0) and A is abbreviated as respectivelyst0With
Further, the step S300 is specifically included：
Step S301, it is to spatial-temporal integration covariance matrixCarry out characteristic value Decomposition obtains signal subspace E；Wherein E=[e1 e2 … eP], eiIt is the main characteristic vector corresponding to i-th of dominant eigenvalue, i Span be [1,2, P], and i is integer, and P is the number of dominant eigenvalue；
Step S302, according to signal subspace E, its orthogonal complement space is obtainedAndWherein, ast0By a definite date The actual steering vector of target echo signal is hoped,For clutter plus noise subspace.
Eigenvalues Decomposition is carried out to the spatial-temporal integration covariance matrix in step S202, obtains signal subspace, clutter adds Noise subspace.By Orthogonal Subspaces characteristic, the actual steering vector of expectation target echo-signal should be empty with clutter plus noise Between it is orthogonal, i.e.,
In formula (3), ast0It is expected the actual steering vector of target echo signal,For clutter plus noise subspace.
Further, the step S400 is specifically included：
Step S401, according to the power output after Beam-former clutter reduction and noiseAnd Desired signal power output criterion is maximized, the object function and constraints for determining steering vector estimator are：
Wherein,For F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M launches for each bay Pulse number,K is the sampling snap number to echo-signal；
Step S402, solved to obtain the actual steering vector of target echo signal according to SDP Relaxation method
When establishing the object function and constraints of steering vector estimator, Beam-former clutter reduction and noise it Power output afterwards is expressed as：
In formula (4),It is the array covariance matrix value of input signal, and
Steering vector estimator object function maximizes σ using desired signal power output criterion is maximizedoutOr most SmallizationSteering vector estimator constraints not only needs to meet formula (4), and the steering vector that needs restraint Norm, even
In formula (5), | | | | represent the l of vector2Norm, N are radar antenna array element number, and M is each bay Launch pulse number.
Constraints in step S401It is non-convex form, here will in the form of Semidefinite Programming It is converted into convex form, and formula (5) is equivalent to
tr(A0)=MN (6)
In formula (6), the mark of tr () representing matrix, andIdeally, matrix A0Order be equal to 1, That is rank (A0)=1, rank () is represented to Matrix Calculating order computing.
Similar,It can be converted into
In formula (7),
Further, formula (7) can be expressed as：
In formula (8),Meanwhile constraintsAlso equivalently it is expressed as
Equally, in the object function and constraints of steering vector estimatorIt is equivalent toCause This, steering vector estimator model is further converted to：
Rank (the A in formula (10)0)=1 is still non-convex constraint, and it is A to be relaxed0>=0, formula (10) relaxation is：
The solution of above formula is tried to achieve using CVX tool boxesAfterwards, the actual steering vector estimate of expectation target echo-signalCan with fromIn extract.
Specifically, in the step S500, according toDraw the weight coefficient of array antenna
In step S402, the actual steering vector estimate of expectation target echo-signal is obtainedAfterwards, using MVDR Algorithm (i.e. the undistorted method of minimum variance) enters row constraint to echo-signal, then make it that array output power is minimum, so as to protect Clutter reduction signal while protecting expectation target echo-signal.The algorithm is expressed as follows：
Formula (12) is solved using method of Lagrange multipliers, the weight coefficient ω of array antenna is obtained, is expressed as
It can be seen that the present invention can obtain the optimal estimation value of expectation target steering vector so that Beam-former is in success On the premise of clutter reduction, wave beam only is formed in expectation target direction, avoids the amplification to noise power, so as to further expand The output Signal to Interference plus Noise Ratio of big Beam-former.
Based on above method embodiment, present invention also offers a kind of sane space-time of the airborne radar under steering vector mismatch Beam Forming System.As shown in Fig. 2 the sane space-time Beam Forming System of airborne radar under the steering vector mismatch, including：
Initialization module 100, for initializing the flying height of airborne platform, speed and the arrival of target echo signal Angle, and determine the Doppler frequency of radar echo signal；
Matrix builds module 200, is reached for establishing the receipt signal model of array antenna, and according to radar echo signal The estimate of angle and Doppler frequency builds spatial-temporal integration covariance matrix；
Subspace acquisition module 300, for according to spatial-temporal integration covariance matrix, determining clutter plus noise subspace；
Steering vector acquisition module 400, for establishing the object function and constraints of steering vector estimator, and according to SDP Relaxation method solves to obtain the actual steering vector of target echo signal；
Weight coefficient acquisition module 500, for according to the undistorted method of minimum variance, obtaining the weights system of array antenna Number.
Further, in the sane space-time Beam Forming System of airborne radar under the steering vector mismatch, the square Battle array structure module 200 specifically includes：
Model establishes unit, for establishing array antenna received signals model x (t)=ast(θ0,fd0)s(t)+ncn(t)； Wherein, s (t) be expectation target echo-signal, ast(θ0,fd0) it is space-time steering vector, ncn(t) sky is added for land clutter signal Between white noise；
Matrix acquiring unit, for being Θ when the space angle section that is located at of note echo-signal angle of arrival, Doppler frequency Section is F, then building spatial-temporal integration covariance matrix according to the estimate of radar echo signal angle of arrival and Doppler frequency is
Further, in the sane space-time Beam Forming System of airborne radar under the steering vector mismatch, the son Space acquisition module 300 specifically includes：
Resolving cell.For being to spatial-temporal integration covariance matrixCarry out special Value indicative decomposes to obtain signal subspace E；Wherein E=[e1 e2 … eP], eiMain feature corresponding to i-th of dominant eigenvalue to Amount, i span is [1,2, P], and i is integer, and P is the number of dominant eigenvalue；
Orthogonal cells, for according to signal subspace E, obtaining its orthogonal complement spaceAnd
Further, it is described to lead in the sane space-time Beam Forming System of airborne radar under the steering vector mismatch Specifically included to vector acquisition module 400：
Steering vector estimator acquiring unit, for according to the power output after Beam-former clutter reduction and noiseAnd desired signal power output criterion is maximized, determine the object function peace treaty of steering vector estimator Beam condition is：
WhereinFor F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M launches for each bay Pulse number,K is the sampling snap number to echo-signal；
Actual steering vector solves unit, for being solved to obtain the reality of target echo signal according to SDP Relaxation method Steering vector
Further, in the sane space-time Beam Forming System of airborne radar under the steering vector mismatch, the power Basis in value coefficient acquisition module 500Draw the weight coefficient of array antenna
In summary, the invention provides the sane space-time Beamforming Method of the airborne radar under steering vector mismatch and it is System, method include：The angle of arrival of the flying height of airborne platform, speed and target echo signal is initialized, and determines that radar returns The Doppler frequency of ripple signal；The receipt signal model of array antenna is established, and according to radar echo signal angle of arrival and Duo Pu Strangle the estimate structure spatial-temporal integration covariance matrix of frequency；According to spatial-temporal integration covariance matrix, clutter plus noise is determined Space；The object function and constraints of steering vector estimator are established, and solves to obtain target according to SDP Relaxation method The actual steering vector of echo-signal；According to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.Energy of the present invention Enough obtain the optimal estimation value of expectation target steering vector so that Beam-former only exists on the premise of success clutter reduction Expectation target direction forms wave beam, avoids the amplification to noise power, so as to further expand the output letter of Beam-former Dry ratio of making an uproar.
It is understood that for those of ordinary skills, can be with technique according to the invention scheme and this hair Bright design is subject to equivalent substitution or change, and all these changes or replacement should all belong to the guarantor of appended claims of the invention Protect scope.

Claims (10)

  1. A kind of 1. sane space-time Beamforming Method of airborne radar under steering vector mismatch, it is characterised in that methods described bag Include following steps：
    A, the angle of arrival of the flying height of initialization airborne platform, speed and target echo signal, and determine radar echo signal Doppler frequency；
    B, the receipt signal model of array antenna is established, and according to radar echo signal angle of arrival and the estimate of Doppler frequency Build spatial-temporal integration covariance matrix；
    C, according to spatial-temporal integration covariance matrix, clutter plus noise subspace is determined；
    D, the object function and constraints of steering vector estimator are established, and solves to obtain target according to SDP Relaxation method The actual steering vector of echo-signal；
    E, according to the undistorted method of minimum variance, the weight coefficient of array antenna is obtained.
  2. 2. the sane space-time Beamforming Method of airborne radar according to claim 1 under steering vector mismatch, its feature exist In the step B is specifically included：
    B1, establish array antenna received signals model x (t)=ast(fd0,θ0)s(t)+ncn(t)；Wherein, s (t) is expectation target Echo-signal, ast(fd0,θ0) it is space-time steering vector, ncn(t) space white noise is added for land clutter signal；
    The space angle section that B2, note echo-signal angle of arrival are located at is Θ, and Doppler frequency section is F, then according to radar return The estimate of direction of arrival and Doppler frequency builds spatial-temporal integration covariance matrix
    Wherein, ast(fd, θ) and expression frequency is fdAnd space angle be θ space-time steering vector, wherein fdFor Doppler frequency area Between frequency values in the range of F, θ is an angle value in the range of the Θ of space angle section.
  3. 3. the sane space-time Beamforming Method of airborne radar according to claim 2 under steering vector mismatch, its feature exist In the step C is specifically included：
    C1, to spatial-temporal integration covariance matrixCarry out Eigenvalues Decomposition and obtain signal Subspace E；Wherein E=[e1e2…eP], ei is the main characteristic vector corresponding to i-th of dominant eigenvalue, i span be [1, 2 ... ..., P], and i is integer, P is the number of dominant eigenvalue；
    C2, according to signal subspace E, obtain its orthogonal complement spaceAndWherein, ast0It is expected target echo letter Number actual steering vector,For clutter plus noise subspace.
  4. 4. the sane space-time Beamforming Method of airborne radar according to claim 3 under steering vector mismatch, its feature exist In the step D is specifically included：
    D1, according to the power output after Beam-former clutter reduction and noiseAnd maximize and it is expected letter Number power output criterion, the object function and constraints for determining steering vector estimator are：
    <mrow> <mtable> <mtr> <mtd> <mrow> <munder> <mi>min</mi> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> </munder> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>E</mi> <mo>~</mo> </mover> <mi>H</mi> </msup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;le;</mo> <mo>|</mo> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;Element;</mo> <mover> <mi>F</mi> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> <mi>&amp;theta;</mi> <mo>&amp;Element;</mo> <mover> <mi>&amp;Theta;</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
    WhereinFor F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M is that each bay launches umber of pulse Mesh,K is the sampling snap number to echo-signal；
    D2, solved according to SDP Relaxation method to obtain the actual steering vector of target echo signal
  5. 5. the sane space-time Beamforming Method of airborne radar according to claim 4 under steering vector mismatch, its feature exist In basis in the step EDraw the weight coefficient of array antenna
  6. A kind of 6. sane space-time Beam Forming System of airborne radar under steering vector mismatch, it is characterised in that including：
    Initialization module, for initializing the flying height of airborne platform, speed and the angle of arrival of target echo signal, and determine The Doppler frequency of radar echo signal；
    Matrix builds module, for establishing the receipt signal model of array antenna, and according to radar echo signal angle of arrival and more The general estimate structure spatial-temporal integration covariance matrix for strangling frequency；
    Subspace acquisition module, for according to spatial-temporal integration covariance matrix, determining clutter plus noise subspace；
    Steering vector acquisition module, established rules for establishing the object function and constraints of steering vector estimator, and according to half Method of relaxation is drawn to solve to obtain the actual steering vector of target echo signal；
    Weight coefficient acquisition module, for according to the undistorted method of minimum variance, obtaining the weight coefficient of array antenna.
  7. 7. the sane space-time Beam Forming System of airborne radar according to claim 6 under steering vector mismatch, its feature exist In the matrix structure module specifically includes：
    Model establishes unit, for establishing array antenna received signals model x (t)=ast(fd0,θ0)s(t)+ncn(t)；Wherein, s (t) it is the echo-signal of expectation target, ast(fd0,θ0) it is space-time steering vector, ncn(t) space white noise is added for land clutter signal Sound；
    Matrix acquiring unit, for being Θ when the space angle section that is located at of note echo-signal angle of arrival, Doppler frequency section For F, then building spatial-temporal integration covariance matrix according to the estimate of radar echo signal angle of arrival and Doppler frequency is
    Wherein, ast(fd, θ) and expression frequency is fdAnd space angle be θ space-time steering vector, wherein fdFor Doppler frequency area Between frequency values in the range of F, θ is an angle value in the range of the Θ of space angle section.
  8. 8. the sane space-time Beam Forming System of airborne radar according to claim 7 under steering vector mismatch, its feature exist In the subspace acquisition module specifically includes：
    Resolving cell, for spatial-temporal integration covariance matrixCarry out Eigenvalues Decomposition Obtain signal subspace E；Wherein E=[e1 e2 … eP], ei is the main characteristic vector corresponding to i-th of dominant eigenvalue, and i's takes Value scope is [1,2 ... ..., P], and i is integer, and P is the number of dominant eigenvalue；
    Orthogonal cells, for according to signal subspace E, obtaining its orthogonal complement spaceAndWherein, ast0It is expected The actual steering vector of target echo signal,For clutter plus noise subspace.
  9. 9. the sane space-time Beam Forming System of airborne radar according to claim 8 under steering vector mismatch, its feature exist In the steering vector acquisition module specifically includes：
    Steering vector estimator acquiring unit, for according to the power output after Beam-former clutter reduction and noiseAnd desired signal power output criterion is maximized, determine the object function peace treaty of steering vector estimator Beam condition is：
    <mrow> <mtable> <mtr> <mtd> <mrow> <munder> <mi>min</mi> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> </munder> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>E</mi> <mo>~</mo> </mover> <mi>H</mi> </msup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> </msub> <mo>|</mo> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;le;</mo> <mo>|</mo> <msubsup> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> <mn>0</mn> </mrow> <mi>H</mi> </msubsup> <msub> <mi>a</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>,</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;Element;</mo> <mover> <mi>F</mi> <mo>&amp;OverBar;</mo> </mover> <mo>,</mo> <mi>&amp;theta;</mi> <mo>&amp;Element;</mo> <mover> <mi>&amp;Theta;</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
    WhereinFor F supplementary set,For Θ supplementary set, N is radar antenna array element number, and M is that each bay launches umber of pulse Mesh,K is the sampling snap number to echo-signal；
    Actual steering vector solves unit, for being solved to obtain the actual guiding of target echo signal according to SDP Relaxation method Vector
  10. 10. the sane space-time Beam Forming System of airborne radar according to claim 9 under steering vector mismatch, its feature exist In basis in the weight coefficient acquisition moduleDraw the weight coefficient of array antenna
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