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 PDFInfo
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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
Technical Field
The invention relates to the technical field of array antennas and airborne radars, in particular to a method and a system for forming a steady space-time beam of an airborne radar under the mismatching of steering vectors.
Background
The main task of airborne radar is to identify and track a desired target in a complex background environment, and therefore, it is necessary to form nulls at ground clutter and form beams at the target. Due to the movement of the airborne platform, the ground clutter spectrum of the airborne phased array radar has the characteristic of broadening of the main clutter in the Doppler frequency domain. In addition, the ground clutter spectrum has a coupling relationship in the space domain and the time domain. Neither conventional time-domain nor spatial-domain filters are capable of forming notches that match ground clutter. Space-Time Adaptive Processing (STAP) technology can jointly suppress ground clutter from an airspace and a Time domain, so that the method is widely applied to detection of ground moving targets by airborne radars. The STAP has both spatial and temporal degrees of freedom, can form notches on spatial spectrum and Doppler frequency domain spectrum planes, effectively suppresses ground clutter, and enhances gain at the target signal direction. However, when there is a deviation between the incident angle of the radar echo signal and the doppler frequency estimation, the signal-to-noise-ratio (SCNR) performance of the STAP output will be severely degraded.
Aiming at the problems, the current common robust adaptive beam forming method comprises an uncertain set-based constraint method and an amplitude response-based constraint method. The idea of uncertain set-based constraints is proposed by scholars such as Vorobyov S a and Gershman a B. The algorithm is based on the ideas of mode constraint and uncertain set constraint, and the worst performance optimization criterion is utilized to realize the maximum improvement on the performance of the beam forming algorithm. Robust beamforming algorithms based on the class of uncertainty set constraints require knowledge of parameters such as the norm boundary of the desired steering vector error or the symmetric positive definite matrix associated with the error, which directly affect the performance of the beamformer. In practice, these parameters are not easy to find accurately. The idea of amplitude response constraint is proposed by scholars such as Yu ZL and Er MH. Because the width of the main beam is increased, noise in a constrained angle interval is received greatly, and the probability that interference is close to the main beam is increased, so that the output signal-to-interference-plus-noise ratio (SINR) is reduced.
Robust beamforming algorithms based on the class of uncertainty set constraints require knowledge of parameters such as the norm boundary of the desired steering vector error or the symmetric positive definite matrix associated with the error, which directly affect the performance of the beamformer. In practice, these parameters are not easy to find accurately. The robust beamforming algorithm based on the amplitude response constraint increases the width of the main beam, so that noise in the constrained angle interval is received greatly, and the probability that interference is close to the main beam is increased, thereby reducing the output SINR.
Thus, there is still a need for improvement and development of the prior art.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a method and a system for forming a robust space-time beam of an airborne radar under the mismatching of steering vectors, and aims to solve the problem that the output signal-to-noise ratio performance of the STAP is seriously reduced when the incident angle of a radar echo signal and the Doppler frequency estimation have deviation in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for forming an airborne radar robust space-time beam under steering vector mismatch, wherein the method comprises the following steps:
A. initializing the flight altitude and speed of an airborne platform and the arrival angle of a target echo signal, and determining the Doppler frequency of a radar echo signal;
B. establishing a receiving signal model of the array antenna, and constructing a space-time integral covariance matrix according to the radar echo signal arrival angle and the estimated value of the Doppler frequency;
C. determining a clutter and noise subspace according to the space-time integral covariance matrix;
D. establishing a target function and a constraint condition of a guide vector estimator, and solving to obtain an actual guide vector of a target echo signal according to a semi-definite programming relaxation method;
E. and acquiring a weight coefficient of the array antenna according to a minimum variance distortionless method.
The method for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises the following steps:
b1, establishing an array antenna receiving signal model x (t) ═ ast(θ0,fd0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(θ0,fd0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
b2, recording the space angle interval where the arrival angle of the echo signal is located is theta, the Doppler frequency interval is F, and constructing a space-time integral covariance matrix according to the estimation values of the arrival angle of the radar echo signal and the Doppler frequency to be theta
The method for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises the following steps:
c1 space-time integral covariance matrix ofDecomposing the eigenvalues to obtain a signal subspace E; wherein E ═ E1e2… eP]，eiIs the main characteristic vector corresponding to the ith main characteristic value, and the value range of i is [1, 2, P ]]And i is an integer, and P is the number of main eigenvalues;
c2 obtaining its orthogonal complement space according to the signal subspace EAnd isWherein, ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
The method for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises the following steps:
d1 output power after clutter and noise suppression from beamformerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
whereinIs the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is the sampling snapshot number of the echo signals;
d2, solving and obtaining the actual guide vector of the target echo signal according to a semi-definite programming relaxation method
The method for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors is characterized in that the method is carried out in the step E according toObtaining the weight coefficient of the array antenna
An airborne radar robust space-time beamforming system under steering vector mismatch, comprising:
the initialization module is used for initializing the flight altitude and speed of the airborne platform and the arrival angle of a target echo signal and determining the Doppler frequency of the radar echo signal;
the matrix construction module is used for establishing a receiving signal model of the array antenna and constructing a space-time integral covariance matrix according to the estimated values of the arrival angle and the Doppler frequency of the radar echo signal;
the subspace acquisition module is used for determining a clutter and noise subspace according to the space-time integral covariance matrix;
the guide vector acquisition module is used for establishing a target function and a constraint condition of the guide vector estimator and solving an actual guide vector of a target echo signal according to a semi-definite programming relaxation method;
and the weight coefficient acquisition module is used for acquiring the weight coefficient of the array antenna according to the minimum variance distortionless method.
The system for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises a matrix construction module and a space-time beam forming module, wherein the matrix construction module specifically comprises:
a model establishing unit for establishing an array antenna receiving signal model x (t) ═ ast(θ0,fd0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(θ0,fd0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
a matrix obtaining unit, configured to, when it is noted that a space angle interval in which an arrival angle of the echo signal is located is Θ and a doppler frequency interval is F, construct a space-time integral covariance matrix as
The system for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises a subspace acquisition module, wherein the subspace acquisition module specifically comprises:
and (5) decomposing the unit. For a space-time integral covariance matrix ofDecomposing the eigenvalues to obtain a signal subspace E; wherein E ═ E1e2… eP]，eiIs the main characteristic vector corresponding to the ith main characteristic value, and the value range of i is[1，2,P]And i is an integer, and P is the number of main eigenvalues;
an orthogonal unit for obtaining the orthogonal complement space of the signal subspace E according to the signal subspace EAnd isWherein, ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
The system for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors comprises a steering vector acquisition module, a steering vector detection module and a control module, wherein the steering vector acquisition module specifically comprises:
a steering vector estimator obtaining unit for obtaining the output power after suppressing clutter and noise according to the beamformerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
whereinIs the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is sampling of echo signalsThe number of snapshots;
an actual guide vector solving unit for solving and obtaining the actual guide vector of the target echo signal according to a semi-definite programming relaxation method
The system for forming the steady space-time beam of the airborne radar under the mismatching of the steering vectors is characterized in that the weight coefficient acquisition module acquires the weight coefficients according toObtaining the weight coefficient of the array antenna
The invention relates to a method and a system for forming steady space-time beams of an airborne radar under mismatching of steering vectors, wherein the method comprises the following steps: initializing the flight altitude and speed of an airborne platform and the arrival angle of a target echo signal, and determining the Doppler frequency of a radar echo signal; establishing a receiving signal model of the array antenna, and constructing a space-time integral covariance matrix according to the radar echo signal arrival angle and the estimated value of the Doppler frequency; determining a clutter and noise subspace according to the space-time integral covariance matrix; establishing a target function and a constraint condition of a guide vector estimator, and solving to obtain an actual guide vector of a target echo signal according to a semi-definite programming relaxation method; and acquiring a weight coefficient of the array antenna according to a minimum variance distortionless method. The invention can obtain the optimal estimated value of the expected target steering vector, so that the beam former only forms the beam in the expected target direction on the premise of successfully suppressing clutter, the amplification of noise power is avoided, and the output signal-to-interference-and-noise ratio of the beam former is further expanded.
Drawings
Fig. 1 is a flowchart of a preferred embodiment of the method for forming a robust space-time beam of an airborne radar under steering vector mismatch according to the present invention.
Fig. 2 is a structural block diagram of a preferred embodiment of the airborne radar robust space-time beamforming system under steering vector mismatch according to the present invention.
Detailed Description
The invention provides a method and a system for forming a steady space-time beam of an airborne radar under mismatching of steering vectors, and in order to make the purpose, the technical scheme and the effect of the invention clearer and clearer, the invention is further described in detail by referring to the attached drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Please refer to fig. 1, which is a flowchart illustrating a method for forming a robust space-time beam of an airborne radar under steering vector mismatch according to a preferred embodiment of the present invention. As shown in FIG. 1, the
S100, initializing the flight altitude and speed of an airborne platform and the arrival angle of a target echo signal, and determining the Doppler frequency of a radar echo signal;
step S200, establishing a receiving signal model of the array antenna, and constructing a space-time integral covariance matrix according to the arrival angle of the radar echo signal and the estimated value of the Doppler frequency;
step S300, determining a clutter and noise subspace according to a space-time integral covariance matrix;
s400, establishing a target function and constraint conditions of a guide vector estimator, and solving to obtain an actual guide vector of a target echo signal according to a semi-definite programming relaxation method;
and S500, acquiring a weight coefficient of the array antenna according to a minimum variance distortionless method.
In the embodiment of the invention, firstly, a space-time integral covariance matrix containing the expected signal guide vector information is constructed according to the estimated expected target arrival angle (DOA) and Doppler frequency. And then, by utilizing the characteristic that the expected signal is orthogonal to the clutter subspace and the noise subspace, deducing the clutter and the noise subspace to serve as a constraint condition of the guide vector estimator. And then, designing an optimal guide vector estimator by adopting guide vector norm constraint and a criterion of maximizing the expected signal power. And converting the quadratic constraint quadratic programming problem into a linear programming problem by adopting a semidefinite programming relaxation method. And finally, establishing a stable space-time beam former by adopting a minimum variance distortionless response criterion, and solving the weight coefficient of each array element of the array antenna.
Specifically, in step S100, the airborne radar is set to operate in a positive side radar mode, that is, the flight direction of the airborne platform is consistent with the plane of the antenna array element. Setting the pulse repetition frequency of the radar to frThe radar wavelength is lambda, the radar height from the ground is H, the flying speed of the airborne platform is v, and the incidence angle of the radar echo signal of the expected target is theta0. Determining the Doppler frequency f of the expected target echo signal according to the parametersd0And is and
specifically, the step S200 specifically includes:
step S201, building an array antenna received signal model x (t) ═ ast(θ0,fd0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(θ0,fd0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
step S202, recording that a space angle interval where an arrival angle of an echo signal is located is theta, a Doppler frequency interval is F, and constructing a space-time integral covariance matrix as
In step S201, a uniform linear array composed of N antenna elements is used, the interval between adjacent antenna elements is λ/2, each array element transmits M coherent pulses, and then a received signal x (t) of the array antenna can be represented as:
x(t)＝ast(θ0,fd0)s(t)+ncn(t) (1)
where s (t) is the echo signal of the desired target, ast(θ0,fd0) Is a space-time steering vector, ncnAnd (t) adding spatial white noise to the ground clutter signal.
ast(θ0,fd0) The method is obtained by solving a Kronecker product (Kronecker product) for a space domain steering vector and a time domain steering vector of a desired target echo signal, namely:
wherein, as(θ0) A spatial steering vector of the desired target echo signalt(fd0) For the time domain steering vector of the desired target echo signal,representing a kronecker product operation. a iss(θ0) And at(fd0) Can be expressed as:
wherein [ ·]TRepresenting the transpose of a vector or matrix, and d is the spacing of adjacent array elements.
In the actual operation of the airborne radar, the estimated arrival angle of the echo signal and the Doppler frequency inevitably deviate. Now, assuming that the space angle interval where the arrival angle of the echo signal is located is theta and the doppler frequency interval is F, a space-time integral covariance matrix is constructed
In formula (2) (.)HRepresenting the conjugate transpose of a vector or matrix. The space-time integral covariance matrix contains the steering vector information of the target echo signal.
When the estimated values of the arrival angle and the Doppler frequency of the radar echo signal have deviation, ast(θ0,fd0) Is further shown asWherein,for the estimation of the angle of arrival with the deviation,for biased doppler frequency estimates, δ is the estimated steering vector error. For convenience of expression, a will be described belowst(θ0,fd0) Andare each abbreviated as ast0And
further, the step S300 specifically includes:
step S301, the space-time integral covariance matrix isDecomposing the eigenvalues to obtain a signal subspace E; wherein E ═ E1e2… eP]，eiIs the main characteristic vector corresponding to the ith main characteristic value, and the value range of i is [1, 2, P ]]And i is an integer, and P is the number of main eigenvalues;
step S302, according to the signal subspace E, obtaining the orthogonal complement space thereofAnd isWherein, ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
And (3) performing eigenvalue decomposition on the space-time integral covariance matrix in the step (S202) to obtain a signal subspace and a clutter and noise subspace. From the subspace orthogonality property, the actual steering vector of the desired target echo signal should be orthogonal to the clutter plus noise subspace, i.e.
In the formula (3), ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
Further, the step S400 specifically includes:
step S401, output power after clutter and noise suppression according to the beam formerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
wherein,is the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is the sampling snapshot number of the echo signals;
step S402, solving and obtaining the actual guide vector of the target echo signal according to a semi-definite programming relaxation method
In establishing the objective function and constraints of the steering vector estimator, the output power after clutter and noise rejection by the beamformer is expressed as:
in the formula (4), the reaction mixture is,is an array covariance matrix estimate of the input signal, and
the steering vector estimator objective function uses the criterion of maximizing the desired signal output power, i.e. maximizing σoutOr minimizeThe constraint condition of the guide vector estimator needs to satisfy not only equation (4) but also the norm of the guide vector, i.e., order
In the formula (5), i | · | | represents l of the vector2Norm, N is the number of radar antenna elements, and M is the number of transmitted pulses of each antenna element.
Constraint conditions in step S401Non-convex form, where it is converted to convex form using a semi-definite programming form, equation (5) being equivalent to
tr(A0)＝MN (6)
In the formula (6), tr (-) represents a trace of the matrix, andideally, matrix A0Is equal to 1, i.e. rank (A)0) Rank () denotes the rank operation on the matrix 1.
In a similar manner, the first and second substrates are,can be converted into
In the formula (7), the reaction mixture is,
further, formula (7) may be represented as:
in the formula (8), the reaction mixture is,at the same time, constraint conditionsIs also equivalently represented as
Also in the objective function and constraints of the steering vector estimatorIs equivalent toTherefore, the steering vector estimator model further translates into:
in formula (10), rank (A)0) 1 is still a non-convex constraint and is relaxed to a0Not less than 0, the relaxation of formula (10) is:
solving the above formula by using CVX tool boxThen, the actual steering vector estimation value of the expected target echo signalCan be selected fromExtracting.
Specifically, in the step S500, according toObtaining the weight coefficient of the array antenna
In step S402, an actual steering vector estimation value of a desired target echo signal is obtainedAnd then, the echo signals are constrained by adopting an MVDR algorithm (namely a minimum variance distortion-free method), and then the output power of the array is minimized, so that clutter signals are suppressed while the expected target echo signals are protected. The expression of the algorithm is as follows:
solving the formula (12) by adopting a Lagrange multiplier method to obtain a weight coefficient omega of the array antenna, which is expressed as
Therefore, the invention can obtain the optimal estimation value of the expected target steering vector, so that the beam former only forms the beam in the expected target direction on the premise of successfully suppressing clutter, the amplification of noise power is avoided, and the output signal-to-interference-and-noise ratio of the beam former is further expanded.
Based on the method embodiment, the invention also provides a system for forming the steady space-time beam of the airborne radar under the mismatching of the steering vector. As shown in fig. 2, the system for forming robust space-time beams of airborne radar under steering vector mismatch includes:
the initialization module 100 is configured to initialize the flying height and the speed of the airborne platform and the arrival angle of the target echo signal, and determine the doppler frequency of the radar echo signal;
the matrix building module 200 is used for building a received signal model of the array antenna and building a space-time integral covariance matrix according to the estimated values of the radar echo signal arrival angle and the Doppler frequency;
a subspace acquisition module 300, configured to determine a clutter plus noise subspace according to a space-time integral covariance matrix;
the guide vector acquisition module 400 is used for establishing a target function and constraint conditions of the guide vector estimator and solving an actual guide vector of the target echo signal according to a semi-definite programming relaxation method;
a weight coefficient obtaining module 500, configured to obtain a weight coefficient of the array antenna according to a minimum variance distortionless method.
Further, in the system for forming a robust space-time beam of an airborne radar under the mismatching of steering vectors, the matrix building module 200 specifically includes:
a model establishing unit for establishing an array antenna receiving signal model x (t) ═ ast(θ0,fd0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(θ0,fd0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
matrix acquisition unitWhen the space angle interval where the arrival angle of the echo signal is located is theta and the Doppler frequency interval is F, a space-time integral covariance matrix is constructed according to the estimation values of the arrival angle and the Doppler frequency of the radar echo signal
Further, in the system for forming a robust space-time beam of an airborne radar under the mismatching of steering vectors, the subspace obtaining module 300 specifically includes:
and (5) decomposing the unit. For a space-time integral covariance matrix ofDecomposing the eigenvalues to obtain a signal subspace E; wherein E ═ E1e2… eP]，eiIs the main characteristic vector corresponding to the ith main characteristic value, and the value range of i is [1, 2, P ]]And i is an integer, and P is the number of main eigenvalues;
an orthogonal unit for obtaining the orthogonal complement space of the signal subspace E according to the signal subspace EAnd is
Further, in the system for forming a robust space-time beam of an airborne radar under the condition of steering vector mismatch, the steering vector obtaining module 400 specifically includes:
a steering vector estimator obtaining unit for obtaining the output power after suppressing clutter and noise according to the beamformerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
whereinIs the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is the sampling snapshot number of the echo signals;
an actual guide vector solving unit for solving and obtaining the actual guide vector of the target echo signal according to a semi-definite programming relaxation method
Further, in the system for forming a robust space-time beam of an airborne radar under the mismatching of the steering vectors, the weight coefficient obtaining module 500 obtains the weight coefficients according toObtaining the weight coefficient of the array antenna
In summary, the present invention provides a method and a system for forming a robust space-time beam of an airborne radar under steering vector mismatch, where the method includes: initializing the flight altitude and speed of an airborne platform and the arrival angle of a target echo signal, and determining the Doppler frequency of a radar echo signal; establishing a receiving signal model of the array antenna, and constructing a space-time integral covariance matrix according to the radar echo signal arrival angle and the estimated value of the Doppler frequency; determining a clutter and noise subspace according to the space-time integral covariance matrix; establishing a target function and a constraint condition of a guide vector estimator, and solving to obtain an actual guide vector of a target echo signal according to a semi-definite programming relaxation method; and acquiring a weight coefficient of the array antenna according to a minimum variance distortionless method. The invention can obtain the optimal estimated value of the expected target steering vector, so that the beam former only forms the beam in the expected target direction on the premise of successfully suppressing clutter, the amplification of noise power is avoided, and the output signal-to-interference-and-noise ratio of the beam former is further expanded.
It should be understood that the technical solutions and concepts of the present invention may be equally replaced or changed by those skilled in the art, and all such changes or substitutions should fall within the protection scope of the appended claims.
Claims (10)
1. A method for forming an airborne radar robust space-time beam under steering vector mismatch is characterized by comprising the following steps:
A. initializing the flight altitude and speed of an airborne platform and the arrival angle of a target echo signal, and determining the Doppler frequency of a radar echo signal;
B. establishing a receiving signal model of the array antenna, and constructing a space-time integral covariance matrix according to the radar echo signal arrival angle and the estimated value of the Doppler frequency;
C. determining a clutter and noise subspace according to the space-time integral covariance matrix;
D. establishing a target function and a constraint condition of a guide vector estimator, and solving to obtain an actual guide vector of a target echo signal according to a semi-definite programming relaxation method;
E. and acquiring a weight coefficient of the array antenna according to a minimum variance distortionless method.
2. The method for forming robust space-time beams of an airborne radar under steering vector mismatch according to claim 1, wherein the step B specifically comprises:
b1, establishing an array antenna receiving signal model x (t) ═ ast(fd0,θ0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(fd0,θ0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
b2, recording the space angle interval where the arrival angle of the echo signal is located is theta, the Doppler frequency interval is F, and constructing a space-time integral covariance matrix according to the estimation values of the arrival angle of the radar echo signal and the Doppler frequency to be theta
Wherein, ast(fdAnd θ) represents a frequency fdAnd a space-time steering vector with a space angle theta, where fdIs a frequency value in the range of the doppler frequency interval F, and θ is an angle value in the range of the spatial angle interval Θ.
3. The method for forming robust space-time beams of an airborne radar under steering vector mismatch according to claim 2, wherein the step C specifically comprises:
c1 space-time integral covariance matrixDecomposing the eigenvalues to obtain a signal subspace E;wherein E ═ E1e2…eP]Ei is the principal eigenvector corresponding to the ith principal eigenvalue, and the numeric range of i is [1, 2, … …, P]And i is an integer, and P is the number of main eigenvalues;
c2 obtaining its orthogonal complement space according to the signal subspace EAnd isWherein, ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
4. The method for forming robust space-time beams of an airborne radar under steering vector mismatch according to claim 3, wherein the step D specifically comprises:
d1 output power after clutter and noise suppression from beamformerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
<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>&theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&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>&theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&Element;</mo> <mover> <mi>F</mi> <mo>&OverBar;</mo> </mover> <mo>,</mo> <mi>&theta;</mi> <mo>&Element;</mo> <mover> <mi>&Theta;</mi> <mo>&OverBar;</mo> </mover> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
whereinIs the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is the sampling snapshot number of the echo signals;
d2, solving and obtaining the reality of the target echo signal according to a semi-definite programming relaxation methodGuide vector
5. The method for forming robust space-time beams of airborne radar under steering vector mismatch according to claim 4, wherein the step E is performed according toObtaining the weight coefficient of the array antenna
6. An airborne radar robust space-time beamforming system under steering vector mismatch, comprising:
the initialization module is used for initializing the flight altitude and speed of the airborne platform and the arrival angle of a target echo signal and determining the Doppler frequency of the radar echo signal;
the matrix construction module is used for establishing a receiving signal model of the array antenna and constructing a space-time integral covariance matrix according to the estimated values of the arrival angle and the Doppler frequency of the radar echo signal;
the subspace acquisition module is used for determining a clutter and noise subspace according to the space-time integral covariance matrix;
the guide vector acquisition module is used for establishing a target function and a constraint condition of the guide vector estimator and solving an actual guide vector of a target echo signal according to a semi-definite programming relaxation method;
and the weight coefficient acquisition module is used for acquiring the weight coefficient of the array antenna according to the minimum variance distortionless method.
7. The system for forming robust space-time beams for airborne radars under steering vector mismatch according to claim 6, wherein the matrix building module specifically comprises:
a model establishing unit for establishing an array antenna receiving signal model x (t) ═ ast(fd0,θ0)s(t)+ncn(t); where s (t) is the echo signal of the desired target, ast(fd0,θ0) Is a space-time steering vector, ncn(t) adding spatial white noise to the ground clutter signal;
a matrix obtaining unit, configured to, when it is noted that a space angle interval in which an arrival angle of the echo signal is located is Θ and a doppler frequency interval is F, construct a space-time integral covariance matrix as
Wherein, ast(fdAnd θ) represents a frequency fdAnd a space-time steering vector with a space angle theta, where fdIs a frequency value in the range of the doppler frequency interval F, and θ is an angle value in the range of the spatial angle interval Θ.
8. The system for forming robust space-time beams of an airborne radar under steering vector mismatch according to claim 7, wherein the subspace acquisition module specifically comprises:
a decomposition unit for space-time integral covariance matrixDecomposing the eigenvalues to obtain a signal subspace E; wherein E ═ E1e2… eP]Ei is the principal eigenvector corresponding to the ith principal eigenvalue, and the numeric range of i is [1, 2, … …, P]And i is an integer, and P is the number of main eigenvalues;
an orthogonal unit for obtaining the orthogonal complement space of the signal subspace E according to the signal subspace EAnd isWherein, ast0For the actual steering vector of the desired target echo signal,a noise subspace is added to the clutter.
9. The system for forming robust space-time beams of an airborne radar under steering vector mismatch according to claim 8, wherein the steering vector obtaining module specifically comprises:
a steering vector estimator obtaining unit for obtaining the output power after suppressing clutter and noise according to the beamformerAnd maximizing the expected signal output power criterion, and determining the objective function and constraint conditions of the steering vector estimator as follows:
<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>&theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&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>&theta;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&Element;</mo> <mover> <mi>F</mi> <mo>&OverBar;</mo> </mover> <mo>,</mo> <mi>&theta;</mi> <mo>&Element;</mo> <mover> <mi>&Theta;</mi> <mo>&OverBar;</mo> </mover> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
whereinIs the complement of the F, and is,is the complement of theta, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element,k is the sampling snapshot number of the echo signals;
an actual guide vector solving unit for solving and obtaining the actual guide vector of the target echo signal according to a semi-definite programming relaxation method
10. The system for airborne radar robust space-time beamforming under steering vector mismatch according to claim 9, wherein the weight systemIn the number acquisition module according toObtaining the weight coefficient of the array antenna
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