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

Abstract

The present invention provides a method and system for airborne radar robust space-time beamforming under steering vector mismatch. The method includes: initializing the flight altitude and speed of the airborne platform and the angle of arrival of the target echo signal, and determining the multiplicity of the radar echo signal. Puler frequency; establish the receiving signal model of the array antenna, and construct the space-time integral covariance matrix according to the estimated value of the radar echo signal arrival angle and Doppler frequency; according to the space-time integral covariance matrix, determine the clutter plus noise Space; establish the objective function and constraint conditions of the steering vector estimator, and obtain the actual steering vector of the target echo signal by solving it according to the semidefinite programming relaxation method; obtain the weight coefficient of the array antenna according to the minimum variance undistorted method. The invention can obtain the optimal estimated value of the steering vector of the desired target, so that the beamformer successfully suppresses the clutter and only forms the beam in the direction of the desired target, avoiding the amplification of noise power, thereby enlarging the output signal-to-interference-noise ratio of the beamformer.

Description

Airborne Radar Robust Space-Time Beamforming Method and System under Steering Vector Mismatch

technical field

The invention relates to the technical field of array antennas and airborne radars, in particular to a robust space-time beamforming method and system for airborne radars under steering vector mismatch.

Background technique

The main task of airborne radar is to identify and track the desired target in a complex background environment. Therefore, it is necessary to form a null at the ground clutter and form a beam at the target. Due to the movement of the airborne platform, the ground clutter spectrum of the airborne phased array radar shows the characteristics of main clutter broadening 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 space-domain filters are capable of forming a notch that matches ground clutter. Space-Time Adaptive Processing (STAP) technology can jointly suppress ground clutter from two-dimensional airspace and time domain, making it widely used in the detection of ground moving targets by airborne radar. STAP has both space and time degrees of freedom, and can form a notch on the spatial spectrum and Doppler frequency domain spectrum plane to effectively suppress ground clutter while enhancing the gain in the direction of the target signal. However, the output signal-to-clutter-plus-noise ratio (SCNR) performance of STAP will be severely degraded when there is a deviation between the incident angle of the radar echo signal and the Doppler frequency estimate.

To solve the above problems, the commonly used robust adaptive beamforming methods are methods based on uncertain set constraints and methods based on amplitude response constraints. The idea based on uncertain set constraints was proposed by scholars such as Vorobyov S A and Gershman A B. This type of algorithm is based on the ideas of modulus constraints and uncertain set constraints, and uses the worst performance optimal criterion to achieve the maximum improvement on the performance of beamforming algorithms. Robust beamforming algorithms based on uncertain set constraints need to know parameters such as the norm boundary of the expected steering vector error or the symmetric positive definite matrix related to the error, and these parameters directly affect the performance of the beamformer. However, in practice, these parameters are not easy to obtain accurately. The idea based on amplitude response constraints was proposed by scholars such as Yu ZL and Er M H. The robust beamforming algorithm based on the amplitude response constraint increases the main beam width, the noise in the constrained angle interval will be greatly received, and the probability of interference close to the main beam will also increase, resulting in an output signal-to-noise ratio (SINR). interference-plus-noise ratio, SINR) decreased.

Robust beamforming algorithms based on uncertain set constraints need to know parameters such as the norm boundary of the expected steering vector error or the symmetric positive definite matrix related to the error, and these parameters directly affect the performance of the beamformer. However, in practice, these parameters are not easy to obtain accurately. The robust beamforming algorithm based on the amplitude response constraint increases the main beam width, the noise in the constrained angle interval will be received greatly, and the probability of interference approaching the main beam will also increase, resulting in a decrease in the output SINR.

Therefore, the prior art still needs to be improved and developed.

Contents of the invention

In view of the deficiencies in the prior art above, the purpose of the present invention is to provide a robust space-time beamforming method and system for airborne radar under mismatched steering vectors, aiming at solving the problem of the incident angle and multiplicity of radar echo signals in the prior art. When there is a deviation in the Puler frequency estimation, the output signal-to-noise ratio performance of STAP will be severely degraded.

In order to achieve the above object, the present invention has taken the following technical solutions:

A method for airborne radar robust space-time beamforming under steering vector mismatch, wherein the method comprises the following steps:

A. Initialize the flight altitude and speed of the airborne platform and the angle of arrival of the target echo signal, and determine the Doppler frequency of the radar echo signal;

B. Establish the receiving signal model of the array antenna, and construct the space-time integral covariance matrix according to the estimated value of the radar echo signal arrival angle and Doppler frequency;

C. Determine the clutter plus noise subspace according to the space-time integral covariance matrix;

D. Establish the objective function and constraint conditions of the steering vector estimator, and obtain the actual steering vector of the target echo signal by solving according to the semi-definite programming relaxation method;

E. Obtain the weight coefficients of the array antenna according to the minimum variance and distortion-free method.

The airborne radar robust space-time beamforming method under the steering vector mismatch, wherein the step B specifically includes:

B1. Establish an array antenna receiving signal model x(t)= _ast (θ ₀ , f _d0 )s(t)+n _cn (t); where, s(t) is the echo signal of the desired target, and a _st ( θ ₀ , f _d0 ) is the space-time steering vector, n _cn (t) is ground clutter signal plus space white noise;

B2, note that the space angle interval where the echo signal angle of arrival is located is Θ, and the Doppler frequency interval is F, then construct the space-time integral covariance matrix according to the estimated value of the radar echo signal angle of arrival and Doppler frequency as

The airborne radar robust space-time beamforming method under the steering vector mismatch, wherein the step C specifically includes:

C1. The space-time integral covariance matrix is Perform eigenvalue decomposition to obtain the signal subspace E; where E=[e ₁ e ₂ ... e _P ], e _i is the main eigenvector corresponding to the i-th main eigenvalue, and the value range of i is [1, 2, P], and i is an integer, and P is the number of main eigenvalues;

C2. According to the signal subspace E, obtain its orthogonal complement space and Among them, _ast0 is the actual steering vector of the expected target echo signal, is the clutter-plus-noise subspace.

The airborne radar robust space-time beamforming method under the steering vector mismatch, wherein, the step D specifically includes:

D1. Output power after suppressing clutter and noise according to the beamformer And maximize the expected signal output power criterion, determine the objective function and constraints of the steering vector estimator as:

in is the complement of F, is the complement of Θ, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element, K is the number of sampling snapshots of the echo signal;

D2. According to the semi-definite programming relaxation method, the actual steering vector of the target echo signal is obtained

The airborne radar robust space-time beamforming method under the steering vector mismatch, wherein, in the step E according to Get the weight coefficient of the array antenna

An airborne radar robust space-time beamforming system under steering vector mismatch, including:

The initialization module is used to initialize the flying height and speed of the airborne platform and the angle of arrival of the target echo signal, and determine the Doppler frequency of the radar echo signal;

The matrix construction module is used to establish the receiving signal model of the array antenna, and constructs the space-time integral covariance matrix according to the estimated value of the arrival angle of the radar echo signal and the Doppler frequency;

The subspace acquisition module is used to determine the clutter plus noise subspace according to the space-time integral covariance matrix;

The steering vector acquisition module is used to establish the objective function and constraint conditions of the steering vector estimator, and solve the actual steering vector of the target echo signal according to the semi-definite programming relaxation method;

The weight coefficient obtaining module is used to obtain the weight coefficient of the array antenna according to the minimum variance non-distortion method.

The airborne radar robust space-time beamforming system under the steering vector mismatch, wherein, the matrix construction module specifically includes:

The model building unit is used to establish the array antenna receiving signal model x(t)= _ast (θ ₀ ,f _d0 )s(t)+n _cn (t); wherein, s(t) is the echo signal of the desired target , a _st (θ ₀ ,f _d0 ) is the space-time steering vector, n _cn (t) is the ground clutter signal plus space white noise;

The matrix acquisition unit is used to construct the space-time integration agreement according to the estimated value of the radar echo signal angle of arrival and the Doppler frequency when the space angle interval where the echo signal angle of arrival is located is Θ and the Doppler frequency interval is F. The variance matrix is

The airborne radar robust space-time beamforming system under the steering vector mismatch, wherein the subspace acquisition module specifically includes:

Decomposition unit. The covariance matrix for space-time integration is Perform eigenvalue decomposition to obtain the signal subspace E; where E=[e ₁ e ₂ ... e _P ], e _i is the main eigenvector corresponding to the i-th main eigenvalue, and the value range of i is [1, 2, P], and i is an integer, and P is the number of main eigenvalues;

The orthogonal unit is used to obtain its orthogonal complement space according to the signal subspace E and Among them, _ast0 is the actual steering vector of the expected target echo signal, is the clutter-plus-noise subspace.

The airborne radar robust space-time beamforming system under the steering vector mismatch, wherein the steering vector acquisition module specifically includes:

Steering vector estimator acquisition unit for output power after clutter and noise suppression according to beamformer And maximize the expected signal output power criterion, determine the objective function and constraints of the steering vector estimator as:

in is the complement of F, is the complement of Θ, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element, K is the number of sampling snapshots of the echo signal;

The actual steering vector solving unit is used to solve the actual steering vector of the target echo signal according to the semi-definite programming relaxation method

The airborne radar robust space-time beamforming system under the steering vector mismatch, wherein, the weight coefficient acquisition module is based on Get the weight coefficient of the array antenna

The airborne radar robust space-time beamforming method and system under steering vector mismatch according to the present invention, the method includes: initializing the flying height and speed of the airborne platform and the angle of arrival of the target echo signal, and determining the radar echo signal Doppler frequency; establish the receiving signal model of the array antenna, and construct the space-time integral covariance matrix according to the estimated value of the radar echo signal arrival angle and Doppler frequency; determine the clutter plus noise according to the space-time integral covariance matrix Subspace; establish the objective function and constraint conditions of the steering vector estimator, and solve the actual steering vector of the target echo signal according to the semidefinite programming relaxation method; obtain the weight coefficient of the array antenna according to the minimum variance undistorted method. The invention can obtain the optimal estimated value of the steering vector of the desired target, so that the beamformer can only form the beam in the direction of the desired target under the premise of successfully suppressing the clutter, avoiding the amplification of the noise power, thereby further expanding the beamformer Output SINR.

Description of drawings

FIG. 1 is a flow chart of a preferred embodiment of the airborne radar robust space-time beamforming method under steering vector mismatch according to the present invention.

FIG. 2 is a structural block diagram of a preferred embodiment of an airborne radar robust space-time beamforming system under steering vector mismatch according to the present invention.

Detailed ways

The present invention provides an airborne radar robust space-time beamforming method and system under steering vector mismatch. In order to make the purpose, technical solution and effect of the present invention clearer and clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

Please refer to FIG. 1 , which is a flow chart of a preferred embodiment of the airborne radar robust space-time beamforming method under steering vector mismatch according to the present invention. As shown in Figure 1, the

Step S100, initializing the flight altitude and speed of the airborne platform and the angle of arrival of the target echo signal, and determining the Doppler frequency of the 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 estimated value of the angle of arrival of the radar echo signal and the Doppler frequency;

Step S300, determining the clutter-plus-noise subspace according to the space-time integral covariance matrix;

Step S400, establishing the objective function and constraint conditions of the steering vector estimator, and obtaining the actual steering vector of the target echo signal by solving according to the semidefinite programming relaxation method;

Step S500 , according to the minimum variance non-distortion method, obtain the weight coefficients of the array antenna.

In the embodiment of the present invention, first, according to the estimated expected target angle of arrival (direction-of-arrival, DOA) and Doppler frequency, a space-time integral covariance matrix including the information of the expected signal steering vector is constructed. Then, the clutter-plus-noise subspace is deduced by using the orthogonal property of the desired signal, clutter and noise subspaces, and used as a constraint condition of the steering vector estimator. Then, an optimal steering vector estimator is designed by using the steering vector norm constraint and the criterion of maximizing the expected signal power. The semidefinite programming relaxation method is used to transform the quadratic constrained quadratic programming problem into a linear programming problem. Finally, a robust space-time beamformer is established by using the minimum-variance distortion-free response criterion, and the weight coefficients of each element of the array antenna are calculated.

Specifically, in step S100 , the airborne radar is set to work in the front and side radar mode, that is, the flight direction of the airborne platform is consistent with the plane of the antenna elements. Set the pulse repetition frequency of the radar as f _r , the radar wavelength as λ, the height of the radar from the ground as H, the flight speed of the airborne platform as v, and the incident angle of the radar echo signal of the desired target as θ ₀ . Determine the Doppler frequency f _d0 of the desired target echo signal according to the above parameters, and

Specifically, the step S200 specifically includes:

Step S201, establishing an array antenna receiving signal model x(t)=a _st (θ ₀ ,f _d0 )s(t)+n _cn (t); wherein, s(t) is the echo signal of the desired target, and a _st (θ ₀ , f _d0 ) is the space-time steering vector, n _cn (t) is the ground clutter signal plus space white noise;

Step S202, remember that the space angle interval where the echo signal angle of arrival is located is Θ, and the Doppler frequency interval is F, then construct the space-time integral covariance matrix according to the estimated value of the radar echo signal angle of arrival and Doppler frequency as

In step S201, a uniform linear array composed of N antenna elements is adopted, the interval between adjacent array elements is λ/2, and each array element transmits M coherent pulses, then the received signal x(t) of the array antenna can be Expressed as:

x(t)＝a _st (θ ₀ ,f _d0 )s(t)+n _cn (t) (1)

Among them, s(t) is the echo signal of the desired target, _ast (θ ₀ , f _d0 ) is the space-time steering vector, and n _cn (t) is the ground clutter signal plus spatial white noise.

a _st (θ ₀ , f _d0 ) is obtained by calculating the Kronecker product (Kronecker product) of the spatial domain steering vector and time domain steering vector of the desired target echo signal, namely:

Among them, a _s (θ ₀ ) is the spatial domain steering vector of the desired target echo signal, at ( _{f d0} ) is the time domain steering vector of the desired target echo signal, Represents the Kronecker product operation. a _s (θ ₀ ) and a _t (f _d0 ) can be expressed as:

Among them, [ ] ^T represents the transposition of a vector or matrix, and d is the interval between adjacent array elements.

Due to the actual work of airborne radar, the estimated angle of arrival and Doppler frequency of the echo signal will inevitably deviate. Now assuming that the angle of arrival of the echo signal is located in the space angle interval Θ, and the Doppler frequency interval is F, then construct a space-time integration covariance matrix

In formula (2), (·) ^H represents 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 there is a deviation between the estimated angle of arrival of the radar echo signal and the Doppler frequency, _ast (θ ₀ ,f _d0 ) is further expressed as in, is the estimated value of the angle of arrival with bias, is the biased Doppler frequency estimate, and δ is the estimated steering vector error. For the convenience of expression, a _st (θ ₀ ,f _d0 ) and are abbreviated as a _st0 and

Further, the step S300 specifically includes:

Step S301, the space-time integral covariance matrix is Perform eigenvalue decomposition to obtain the signal subspace E; where E=[e ₁ e ₂ ... e _P ], e _i is the main eigenvector corresponding to the i-th main eigenvalue, 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, obtain its orthogonal complement space and Among them, _ast0 is the actual steering vector of the expected target echo signal, is the clutter-plus-noise subspace.

Eigenvalue decomposition is performed on the space-time integral covariance matrix in step S202 to obtain a signal subspace and a clutter plus noise subspace. Due to the subspace orthogonality, the actual steering vector of the desired target echo signal should be orthogonal to the clutter plus noise subspace, that is,

In formula (3), a _st0 is the actual steering vector of the desired target echo signal, is the clutter-plus-noise subspace.

Further, the step S400 specifically includes:

Step S401, output power after suppressing clutter and noise according to the beamformer And maximize the expected signal output power criterion, determine the objective function and constraints of the steering vector estimator as:

in, is the complement of F, is the complement of Θ, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element, K is the number of sampling snapshots of the echo signal;

Step S402, obtain the actual steering vector of the target echo signal by solving according to the semidefinite programming relaxation method

When establishing the objective function and constraints of the steering vector estimator, the output power of the beamformer after suppressing clutter and noise is expressed as:

In formula (4), is the array covariance matrix estimate of the input signal, and

The objective function of the steering vector estimator adopts the criterion of maximizing the expected signal output power, that is, maximizing σ _out or minimizing The constraint condition of the steering vector estimator not only needs to satisfy formula (4), but also needs to constrain the norm of the steering vector, that is,

In formula (5), ||·|| represents the l ₂ norm of the vector, N is the number of radar antenna elements, and M is the number of pulses transmitted by each antenna element.

Constraints in step S401 It is a non-convex form. Here, it is transformed into a convex form by semi-definite programming. Formula (5) is equivalent to

tr(A ₀ )=MN (6)

In Equation (6), tr( ) represents the trace of the matrix, and Ideally, the rank of the matrix A ₀ is equal to 1, that is, rank(A ₀ )=1, and rank(·) represents an operation to rank the matrix.

akin, can be converted to

In formula (7),

Further, formula (7) can be expressed as:

In formula (8), At the same time, the constraints is also equivalently expressed as

Likewise, in the objective function and constraints of the steering vector estimator Equivalent to Therefore, the steering vector estimator model is further transformed into:

In formula (10), rank(A ₀ )=1 is still a non-convex constraint, and it is relaxed to A ₀ ≥ 0, and formula (10) is relaxed as:

Use the CVX toolbox to find the solution of the above formula After that, the actual steering vector estimate of the desired target echo signal is then you can start from extracted from.

Specifically, in the step S500, according to Get the weight coefficient of the array antenna

In step S402, the actual steering vector estimated value of the desired target echo signal is obtained Afterwards, the MVDR algorithm (minimum variance and distortion-free method) is used to constrain the echo signal, and then the output power of the array is minimized, so as to protect the expected target echo signal and suppress the clutter signal at the same time. The algorithm is expressed as follows:

Using the Lagrange multiplier method to solve equation (12), the weight coefficient ω of the array antenna is obtained, expressed as

It can be seen that the present invention can obtain the optimal estimated value of the steering vector of the desired target, so that the beamformer can only form the beam in the direction of the desired target under the premise of successfully suppressing the clutter, avoiding the amplification of the noise power, thereby further expanding the beamforming The signal-to-interference-noise ratio of the output of the device.

Based on the above method embodiments, the present invention also provides an airborne radar robust space-time beamforming system under steering vector mismatch. As shown in Figure 2, the airborne radar robust space-time beamforming system under the steering vector mismatch includes:

The initialization module 100 is used to initialize the flight height, speed and angle of arrival of the target echo signal of the airborne platform, and determine the Doppler frequency of the radar echo signal;

The matrix construction module 200 is used to establish the received signal model of the array antenna, and constructs a space-time integral covariance matrix according to the estimated value of the angle of arrival of the radar echo signal and the Doppler frequency;

The subspace acquisition module 300 is used to determine the clutter plus noise subspace according to the space-time integral covariance matrix;

The steering vector acquisition module 400 is used to establish the objective function and constraint conditions of the steering vector estimator, and obtain the actual steering vector of the target echo signal by solving according to the semidefinite programming relaxation method;

The weight coefficient obtaining module 500 is configured to obtain the weight coefficient of the array antenna according to the minimum variance non-distortion method.

Further, in the airborne radar robust space-time beamforming system under the steering vector mismatch, the matrix construction module 200 specifically includes:

The model building unit is used to establish the array antenna receiving signal model x(t)= _ast (θ ₀ ,f _d0 )s(t)+n _cn (t); wherein, s(t) is the echo signal of the desired target , a _st (θ ₀ ,f _d0 ) is the space-time steering vector, n _cn (t) is the ground clutter signal plus space white noise;

The matrix acquisition unit is used to construct the space-time integration agreement according to the estimated value of the radar echo signal angle of arrival and the Doppler frequency when the space angle interval where the echo signal angle of arrival is located is Θ and the Doppler frequency interval is F. The variance matrix is

Further, in the airborne radar robust space-time beamforming system under the steering vector mismatch, the subspace acquisition module 300 specifically includes:

Decomposition unit. The covariance matrix for space-time integration is Perform eigenvalue decomposition to obtain the signal subspace E; where E=[e ₁ e ₂ ... e _P ], e _i is the main eigenvector corresponding to the i-th main eigenvalue, and the value range of i is [1, 2, P], and i is an integer, and P is the number of main eigenvalues;

The orthogonal unit is used to obtain its orthogonal complement space according to the signal subspace E and

Further, in the airborne radar robust space-time beamforming system under the steering vector mismatch, the steering vector acquisition module 400 specifically includes:

Steering vector estimator acquisition unit for output power after clutter and noise suppression according to beamformer And maximize the expected signal output power criterion, determine the objective function and constraints of the steering vector estimator as:

in is the complement of F, is the complement of Θ, N is the number of radar antenna elements, M is the number of pulses transmitted by each antenna element, K is the number of sampling snapshots of the echo signal;

The actual steering vector solving unit is used to solve the actual steering vector of the target echo signal according to the semi-definite programming relaxation method

Further, in the airborne radar robust space-time beamforming system under the steering vector mismatch, the weight coefficient acquisition module 500 is based on Get the weight coefficient of the array antenna

In summary, the present invention provides a method and system for airborne radar robust space-time beamforming under steering vector mismatch. The Doppler frequency of the echo signal; establish the receiving signal model of the array antenna, and construct the space-time integration covariance matrix according to the estimated value of the radar echo signal arrival angle and Doppler frequency; according to the space-time integration covariance matrix, determine Clutter plus noise subspace; establish the objective function and constraint conditions of the steering vector estimator, and obtain the actual steering vector of the target echo signal by solving it according to the semidefinite programming relaxation method; obtain the weight of the array antenna according to the minimum variance undistorted method coefficient. The invention can obtain the optimal estimated value of the steering vector of the desired target, so that the beamformer can only form the beam in the direction of the desired target under the premise of successfully suppressing the clutter, avoiding the amplification of the noise power, thereby further expanding the beamformer Output SINR.

It can be understood that those skilled in the art can make equivalent replacements or changes according to the technical solutions of the present invention and the concept of the present invention, and all these changes or replacements should belong to the protection scope of the appended claims of the present invention.

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) ═ a_st(f_d0,θ₀)s(t)+n_cn(t); where s (t) is the echo signal of the desired target, a_st(f_d0,θ₀) Is a space-time steering vector, n_cn(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, a_st(f_dAnd θ) represents a frequency f_dAnd a space-time steering vector with a space angle theta, where f_dIs 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…e_P]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, a_st0For 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:

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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) ═ a_st(f_d0,θ₀)s(t)+n_cn(t); where s (t) is the echo signal of the desired target, a_st(f_d0,θ₀) Is a space-time steering vector, n_cn(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, a_st(f_dAnd θ) represents a frequency f_dAnd a space-time steering vector with a space angle theta, where f_dIs 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… e_P]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, a_st0For 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:

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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