CN105044693A - Microwave associated imaging radar amplitude-phase error correction method based on auxiliary array elements - Google Patents

Abstract

The invention provides a microwave associated imaging radar amplitude-phase error correction method based on auxiliary array elements so as to estimate a microwave associated imaging radar amplitude-phase error and then obtain a relatively ideal time and space radiation field by compensation on the amplitude-phase error. The method comprises the steps that step 1: a microwave associated imaging radar transmitting antenna array transmits multiple types of waveforms, corresponding multiple types echo data are received by a receiving antenna array, matched filtering is performed on the echo data, and the obtained echo data matrixes are orderly arranged; step 2: the elements in the echo data matrixes are grouped; step 3: a data covariance matrix is estimated; step 4: target angle estimation is performed so that a target direction vector is obtained; step 5: the amplitude error and the phase error of the transmitting antenna array are estimated respectively so that corresponding error estimation values are obtained; and step 6: the amplitude and the phase of the transmitting antenna array are respectively corrected according to the amplitude error estimation value and the phase error estimation value of the transmitting antenna array.

Description

Based on the microwave relevance imaging radar amplitude phase error correction method of auxiliary array element

Technical field

The invention belongs to Radar Technology field, particularly a kind of microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element, is applied to the on line emendation of relevance imaging radar array amplitude phase error.

Background technology

Radar is requisite electronics in the modern life, and wherein microwave relevance imaging radar system can realize the staring imaging for scene, has wide application prospect in scenes such as national defence, anti-terrorism, securities.Launch different signals because microwave relevance imaging radar needs to launch array element in difference, therefore easilier than traditional array radar introduce larger amplitude phase error, amplitude phase error constantly can change along with the environmental factor such as time, temperature simultaneously.When there is amplitude phase error, the space-time radiation field of microwave relevance imaging radar can distort, and this can cause the decline of microwave relevance imaging radar imagery performance or even cannot imaging.Because the amplitude phase error of radar constantly changes along with the environmental factor such as time, temperature, therefore On-line Estimation amplitude phase error is a key issue of microwave relevance imaging radar application effectively.

The microwave relevance imaging system based on thinned array and formation method is disclosed in the patent " microwave relevance imaging system and formation method based on thinned array " (application number 201310167360.6) of Xian Electronics Science and Technology University's application.Relevance imaging theory is extended to microwave regime from optics by the method, and utilizes compressive sensing theory to solve corresponding problem, achieves the imaging effect exceeding Rayleigh diffraction limit.But, the defect of the method does not consider the amplitude phase error of array, when there is amplitude phase error in radar array, transmitting of radar can be subject to the impact of amplitude phase error, there is certain error relative to desirable space-time radiation field in the space-time random radiation field of thus synthesizing in space, this finally can cause the decline of imaging performance or even imaging to fall flat.

Current radar array corrects and mainly utilizes calibration source to carry out alignment technique, can reach the amplitude phase error estimating array more accurately at these.In a lot of practical application scene, because the amplitude phase error of radar array constantly can change along with the environmental factor such as time, temperature, need to correct amplitude phase error online, utilize calibration source to carry out correcting just have significant limitation.

Summary of the invention

For above-mentioned technical matters, the object of the present invention is to provide a kind of microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element, to estimate the amplitude phase error of microwave relevance imaging radar, and then obtain ideal space-time radiation field by compensating amplitude phase error, finally utilize relevance imaging algorithm to reconstruct image field scape.

In order to achieve the above object, the present invention is achieved by the following technical solutions.

Based on a microwave relevance imaging radar amplitude phase error correction method for auxiliary array element, comprise the following steps:

Step 1, the transmitting antenna array of microwave relevance imaging radar launches multiple transmitted waveform, the receiving antenna array of described microwave relevance imaging radar receives corresponding multiple echo data, matched filtering is carried out to described echo data, and order arrangement is carried out to filtered echo data, obtain echo data matrix; Wherein, described receiving antenna array comprises three reception array elements of at right angles arrangement;

Step 2, three according to described rectangular arrangement receive the invariable rotary characteristic that array element obtains described echo data matrix, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix according to described invariable rotary characteristic, and according to described first data selection matrix, the second data selection matrix and the 3rd data selection matrix, the element in described echo data matrix is divided into groups respectively, obtain the first corresponding integrated data, the second integrated data and the 3rd integrated data;

Step 3, estimate the Cross-covariance of the Cross-covariance of the auto-covariance matrix of described first integrated data, described first integrated data and the second integrated data, described first integrated data and the 3rd integrated data respectively, sequential combination is data covariance matrix;

Step 4, utilizes described data covariance matrix to carry out angle on target estimation, obtains the direction vector of target;

Step 5, estimates the range error of described transmitting antenna array and phase error respectively according to the direction vector of described target, obtains range error estimated value and the phase error estimation and phase error value of described transmitting antenna array;

Step 6, according to range error estimated value and the phase error estimation and phase error value of described transmitting antenna array, corrects the amplitude of described transmitting antenna array and phase place respectively.

Preferably, described step 1 comprises following sub-step:

1a) transmitting antenna array of microwave relevance imaging radar comprises M transmitting array element, launches array element for described M and launches multiple transmitted waveform, and m the complex envelope launching the transmitted waveform of array element is s _m, wherein M is natural number, and m is natural number, and m=1 ..., M;

1b) receiving antenna array of microwave relevance imaging radar comprises N number of reception array element, and described N number of reception array element receives corresponding multiple echo data, and the n-th echo data receiving the q subpulse that array element receives is y _{n, q}, wherein N is natural number, and n is natural number, and n=1 ..., N, N=3;

Echo data and described M the conjugation of launching the complex envelope of the transmitted waveform of array element of q subpulse 1c) described N number of reception array element received make inner product, obtain corresponding matched filtering and export x _q, wherein x _q(n-1) M+m element be represent the echo data y receiving the q subpulse that array element receives by described n-th _{n, q}the complex envelope s of the transmitted waveform of array element is launched with m _mconjugation make inner product after, obtain corresponding matched filtering and export, obtained by following formulae discovery:

Wherein, n=1 ..., N; M=1 ..., M; Q=1 ..., Q, Q indicating impulse number of times, M, m, N, n, Q, q are natural number;

1d) matched filtering corresponding for described N number of reception array element output is lined up a column vector according to subscript m and subscript n order successively, obtain the matched filtering result x of q subpulse _q;

Receive array element by n-th and according to subscript m order, a column vector is lined up for the matched filtering Output rusults that M is launched the complex envelope of the transmitted waveform of array element

Will a column vector x is lined up according to subscript n order _q:

Wherein, operational symbol () ^trepresent transpose operation, sign of operation * represents that Khatri-Rao amasss, n _qfor additive white Gaussian noise, b _qfor obeying the target complex scattering coefficients of SwerlingII type, A _rfor receiving antenna array steering vector, A _utfor there being the transmitting antenna array steering vector in amplitude phase error situation;

Described matched filtering result x 1e) Q pulse obtained respectively _qline up a matrix according to subscript q order, obtain the echo data matrix X of Q pulse:

X＝[x ₁，…，x _Q]＝(A _r*A _ut)B+W

Wherein, B represents the target scattering coefficient matrix of Q subpulse, B=[b ₁..., b _q]; W represents the additive white noise matrix of Q subpulse, W=[n1 ..., n _q].

Preferably, described step 2 comprises following sub-step:

2a) obtain the invariable rotary characteristic in described echo data matrix between element according to three reception array elements of described rectangular arrangement, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix respectively according to described invariable rotary characteristic, wherein the first data selection matrix is:

$J_1=\[1,0,0\]\⊗I_M$

Second data selection matrix is:

$J_2=\[0,1,0\]\⊗I_M$

3rd data selection matrix is:

Wherein, I _mfor the unit matrix of M × M dimension, represent that Kronecker amasss;

2b) described first data selection matrix, the second data selection matrix and the 3rd data selection matrix is utilized to select the element in described echo data matrix X and divide into groups respectively, obtain the first corresponding integrated data, comprise the second integrated data of the invariable rotary factor and comprise the 3rd integrated data of the invariable rotary factor, wherein the first integrated data is:

X ₁＝J ₁X＝A _utB+J ₁W

Second integrated data is: X ₂=J ₂x=A _utΛ _xb+J ₂w

3rd integrated data is:

X ₃＝J ₃X＝A _utΛ _yB+J ₃W

Wherein, for the invariable rotary factor relative to x-axis, ${\mathrm{\Λ}}_y=diag(\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{dcos\φ}}_{y,1}},\mathrm{...},e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{dcos\φ}}_{y,P}}\])$ For the invariable rotary factor relative to y-axis.

Preferably, described step 3 comprises following sub-step:

3a) obtain the first integrated data X by following formulae discovery ₁autocorrelation matrix R ₁₁:

$R_{11}=\frac{1}{Q}{X}_1{X_1}^H=A_{ut}{R}_B{A_{ut}}^H+{{\mathrm{\σ}}_n}^2{I}_M$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor having the transmitting antenna array in amplitude phase error situation, σ _n ²for noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix;

3b) by following formula to the first integrated data X ₁autocorrelation matrix R ₁₁carry out Eigenvalues Decomposition, obtain the estimation of noise power

$R_{11}=U_r{\mathrm{\Λ}}_r{U}_r^H$

${{\widehat{\mathrm{\σ}}}_n}^2=\frac{1}{Q}\underset{k=M-Q+1}{\overset{M}{\Σ}}{\mathrm{\λ}}_{r,k}$

Wherein, the diagonal matrix Λ of proper vector formation _r=diag ([λ _{r, 1}, λ _{r, 2}..., λ _{r, M}]), wherein λ _{r, 1}>=λ _{r, 2}>=...>=λ _{r, M}, U _rfor the matrix that proper vector is formed, operational symbol () ^hthe conjugate transpose of representing matrix, Q indicating impulse number, M represents the element number of array of transmitting antenna array;

3c) by the estimation of noise power from the first integrated data X ₁autocorrelation matrix R ₁₁middle deduction, obtains the first integrated data X ₁auto-covariance matrix R _11s:

$R_{11s}=R_{11}-{{\widehat{\mathrm{\σ}}}_n}^2{I}_M\≈A_{ut}{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, for the estimation of noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix;

3d) obtain the first integrated data X by following formulae discovery ₁with the second integrated data X ₂cross-covariance R ₂₁:

$R_{21}=\frac{1}{Q}{X}_2{X_1}^H=A_{ut}{\mathrm{\Λ}}_x{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to x-axis, operational symbol () ^hthe conjugate transpose of representing matrix;

3e) obtain the first integrated data X by following formulae discovery ₁with the 3rd integrated data X ₃cross-covariance R ₃₁:

$R_{31}=\frac{1}{Q}{X}_3{X_1}^H=A_{ut}{\mathrm{\Λ}}_y{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to y-axis, operational symbol () ^hthe conjugate transpose of representing matrix;

3f) by described first integrated data X ₁auto-covariance matrix R _11s, the first integrated data X ₁with the second integrated data X ₂cross-covariance R ₂₁, the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance R ₃₁sequential combination is data covariance matrix.

Preferably, described step 4 comprises following sub-step:

4a) according to following formula pair do svd:

Wherein, R _11sbe the first integrated data X ₁auto-covariance matrix, R ₂₁be the first integrated data X ₁with the second integrated data X ₂cross-covariance, for asking pseudo-inverse operation to accord with, Λ _x=diag ([λ _{x, 1}..., λ _{x, P}]) diagonal matrix that forms for P eigenwert, U _xt=[v _{xt, 1}... v _{xt, P}] matrix that forms for P eigenwert characteristic of correspondence vector;

4b) according to following formula to be set forth in p eigenvalue λ _{x, p}carry out computing, obtain the cone angle φ of p target relative to x-axis _{x, p}:

${\mathrm{\φ}}_{x,p}=arccos\[\∠\left({\mathrm{\λ}}_{x,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression;

4c) according to following formula pair do svd:

Wherein, R ₃₁be the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance, R _11sbe the first integrated data X ₁auto-covariance matrix, for asking pseudo-inverse operation to accord with, Λ _y=diag ([λ _{y, 1}..., λ _{y, P}]) diagonal matrix that forms for P eigenwert, U _yt=[v _{yt, 1}..., v _{yt, P}] matrix that forms for P eigenwert characteristic of correspondence vector;

4d) according to following formula to described p eigenvalue λ _{y, p}operation, can obtain the cone angle φ of p target relative to y-axis _{y, p}:

${\mathrm{\φ}}_{y,p}=arccos\[\∠\left({\mathrm{\λ}}_{y,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression;

4e) corresponding according to following formulae discovery p target direction vector r _p:

$r_p={\[{\mathrm{cos\φ}}_{x,p},{\mathrm{cos\φ}}_{y,p},\sqrt{1-{\cos }^2{\mathrm{\φ}}_{x,p}-{\cos }^2{\mathrm{\φ}}_{y,p}}\]}^T$

Wherein φ _{x, p}be the cone angle of p target relative to x-axis, φ _{y, p}be the cone angle of p target relative to y-axis.

Preferably, described step 5 comprises following sub-step:

The transmitting steering vector a (r of p target time 5a) error free according to following formulae discovery _p):

$a\left(r_p\right)={\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,1}}^T{r}_p},\mathrm{...},e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,M}}^T{r}_p}\]}^T$

Wherein, r _{t, 1}..., r _{t, M}represent the 1st to M position of launching array element respectively, operational symbol () ^trepresent transpose operation;

5b) according to following formula to p proper vector v _{xt, p}normalization, obtains described transmitting steering vector a (r _p) estimation

$\hat{a}\left(r_p\right)=v_{xt,p}/v_{xt,p}\left(1\right),p=1,2,...,P$

Wherein, v _{xt, p}(1) v is represented _{xt, p}the value of first element;

The range error estimated value ρ of array element 5c) is launched according to following formulae discovery m _m:

${\mathrm{\ρ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\left|{\hat{a}}_{p,m}\right|}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, operational symbol || for asking absolute value sign;

The phase error estimation and phase error value ψ of array element 5d) is launched according to following formulae discovery m _m:

${\mathrm{\ψ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\∠\left({\hat{a}}_{p,m}{a}_{p,m}^{*}\right)}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, a _{p, m}for launching steering vector a (r _p) m element, operational symbol () ^*represent conjugate operation.

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

First, the each array element of transmitting antenna array that present invention utilizes microwave relevance imaging radar launches the feature of unlike signal, by auxiliary array element (three receive array element), three groups of data are obtained in receiving end matched filtering, and there is between three groups of data invariable rotary characteristic, the present invention utilizes invariable rotary characteristic from the direction vector extracting target, and estimate the amplitude phase error of microwave relevance imaging radar further, then according to estimating that the amplitude phase error obtained carries out amplitude and phase error correction, obvious the present invention does not need calibration source to participate in carry out amplitude and phase error correction to radar array, therefore implement simple, complexity is low, thus the efficiency of microwave relevance imaging radar amplitude phase error correction can be improved.

The second, the present invention obtains the direction vector of target in step 4, and therefore the present invention can also realize the location for target while realizing amplitude and phase error correction.

3rd, the present invention directly estimates amplitude phase error from echo data, therefore the present invention can carry out on-line correction to amplitude phase error, namely under radar duty, just can carry out amplitude and phase error correction to radar, ensure that the real-time of microwave relevance imaging radar amplitude phase error correction.

4th, the present invention utilizes the amplitude phase error estimated to compensate transmitting antenna array amplitude and phase place, amplitude and phase error correction can be carried out to transmitting antenna array, the transmitting antenna array after correcting is utilized to launch multiple waveforms, space-time random radiation field accurately can be formed in space, thus ensure the imaging accuracy of microwave relevance imaging radar.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of a kind of microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element of the embodiment of the present invention;

Fig. 2 is the schematic diagram of the geometric configuration of the present invention's microwave relevance imaging used radar;

Fig. 3 is the comparison diagram that transmitting antenna array 81 launches range error that array element estimated by the present invention and actual margin error;

Fig. 4 is the comparison diagram that transmitting antenna array 81 launches phase error that array element estimated by the present invention and substantial phase error;

Fig. 5 is microwave relevance imaging original scene figure;

During the fast umber of beats 1000 of Fig. 6, when not carrying out amplitude and phase error correction, utilize the target scene that microwave relevance imaging algorithm recovers;

During the fast umber of beats 1000 of Fig. 7, after utilizing the inventive method to carry out amplitude and phase error correction, the target scene that recycling microwave relevance imaging algorithm recovers.

Embodiment

For enabling above-mentioned purpose of the present invention, feature and advantage become apparent more, and below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

In order to the present invention will be described better, first the geometric configuration of the present invention's microwave relevance imaging used radar is described.With reference to Fig. 2, it is the schematic diagram of the geometric configuration of the present invention's microwave relevance imaging used radar, the present invention is based on the radar system of microwave relevance imaging, comprising: receive array element 1, receive array element 2, receive array element 3, transmitting antenna array 4, target 5 and signal processor 6.Wherein receive array element 1, receive array element 2 and receive array element 3 and be referred to as auxiliary array element.The microwave radiation field utilizing emitting antenna 4 to produce carries out irradiation to target 5 and produces echo, the echoed signal of auxiliary array element receiving target, signal processor 6 processes the amplitude phase error that echoed signal obtains transmitting antenna array 1, signal processor 6 calculates space-time random radiation field according to the amplitude phase error obtained and transmitting of transmitting antenna array 4, and signal processor 6 utilizes the space-time random radiation field calculated and the Received signal strength process receiving array element 1 to obtain the imaging of target.It should be noted that, above-mentioned reception array element is also referred to as receiving antenna.

Described reception array element 1, reception array element 2, reception array element 3 and transmitting antenna array 4 are all co-located on same single base Texas tower, a common formation face battle array.

Described auxiliary array element, namely receive array element 1, receive array element 2 and receive array element 3, they are at right angles arranged, and namely set up rectangular coordinate system to receive array element 1 for initial point, reception array element 2 is distributed in x-axis positive axis, and reception array element 3 is distributed in y-axis positive axis.Receive array element 1 and the spacing received between array element 2 and the spacing d that receives between array element 1 and reception array element 3 all satisfied wherein λ is the wavelength of carrier wave.Auxiliary array element is special antenna, and its magnitude-phase characteristics is known, and does not substantially change with environmental factor.

In Fig. 2, coordinate origin O is set to the position receiving array element 1, receives array element 2 in x-axis positive axis, receives array element 3 in y-axis positive axis.The position angle of p target is θ _p, the angle of pitch is φ _p, be φ relative to the cone angle of x-axis _{x, p}, be φ relative to the cone angle of y-axis _{y, p}, wherein (cos φ _p) ²+ (cos φ _{x, p}) ²+ (cos φ _{y, p}) ²=1.The positional representation of transmitting antenna array m emitting antenna is r _{t, m}=[x _m, y _m, 0] ^t, wherein m=1,2 ... M.

Based on the explanation of the aforementioned geometric configuration to the present invention's microwave relevance imaging used radar, below in conjunction with Fig. 1, the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element of the present invention is described.The described microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element can realize in signal processor in fig. 2.

With reference to Fig. 1, show the process flow diagram of a kind of microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element of the embodiment of the present invention, the present embodiment specifically can comprise the following steps:

Step 1, the transmitting antenna array of microwave relevance imaging radar launches multiple transmitted waveform, the receiving antenna array of described microwave relevance imaging radar receives corresponding multiple echo data, matched filtering is carried out to described echo data, and order arrangement is carried out to filtered echo data, obtain echo data matrix; Wherein, described receiving antenna array comprises three reception array elements of at right angles arrangement.

Described step 1 comprises following sub-step:

1a) transmitting antenna array of microwave relevance imaging radar comprises M transmitting array element, launches array element for described M and launches multiple transmitted waveform, and m the complex envelope launching the transmitted waveform of array element is s _m, wherein M is natural number, and m is natural number, and m=1 ..., M.

It should be noted that, the transmitting antenna array array element that the transmitting antenna array 4 in each transmitting antenna array array element corresponding diagram 2 described in this step comprises.

1b) receiving antenna array of microwave relevance imaging radar comprises N number of reception array element, and described N number of reception array element receives corresponding multiple echo data, and the n-th echo data receiving the q subpulse that array element receives is y _{n, q}, wherein N is natural number, and n is natural number, and n=1 ..., N, N=3.

According to Fig. 2, in the present embodiment, N gets 3, namely microwave relevance imaging radar comprises reception array element 1, receives array element 2 and receive array element 3, and 3 reception array elements are at right angles arranged, namely rectangular coordinate system is set up to receive array element 1 for initial point, receiving array element 2 is distributed in x-axis positive axis, receives array element 3 and is distributed in y-axis positive axis.Receive array element 1 and the spacing received between array element 2 and the spacing d that receives between array element 1 and reception array element 3 all satisfied wherein λ is the wavelength of carrier wave.

According to Fig. 2, utilize microwave relevance imaging radar mockup, each array element of transmitting antenna array 4 launches different waveforms, and the echo data that n-th receives the q subpulse that array element receives is designated as y _{n, q}.

Echo data and described M the conjugation of launching the complex envelope of the transmitted waveform of array element of q subpulse 1c) described N number of reception array element received make inner product, obtain corresponding matched filtering and export x _q, wherein x _q(n-1) M+m element be represent the echo data y receiving the q subpulse that array element receives by described n-th _{n, q}the complex envelope s of the transmitted waveform of array element is launched with m _mconjugation make inner product after, obtain corresponding matched filtering and export, obtained by following formulae discovery:

Wherein, n=1 ..., N; M=1 ..., M; Q=1 ..., Q, Q indicating impulse number of times, M, m, N, n, Q, q are natural number.

1d) matched filtering corresponding for described N number of reception array element output is lined up a column vector according to subscript m and subscript n order successively, obtain the matched filtering result x of q subpulse _q;

Receive array element by n-th and according to subscript m order, a column vector is lined up for the matched filtering Output rusults that M is launched the complex envelope of the transmitted waveform of array element

Will a column vector x is lined up according to subscript n order _q:

Wherein, operational symbol () ^trepresent transpose operation, sign of operation * represents that Khatri-Rao amasss, n _qfor additive white Gaussian noise, b _qfor obeying the target complex scattering coefficients of SwerlingII type, A _rfor receiving antenna array steering vector, A _utfor there being the transmitting antenna array steering vector in amplitude phase error situation.

It should be noted that, the transmitted waveform complex envelope s of the present embodiment and m transmitting antenna array array element _mconjugation carry out matched filtering as inner product, namely by y _{n, q}line up a column vector with the echo data after all M transmitted waveform matched filtering, the matched filtering result receiving array element n can be obtained join end to end according to the matched filtering result of 3 reception array elements again and obtain the matched filtering result x of q subpulse _q.

Described matched filtering result x 1e) Q pulse obtained respectively _qline up a matrix according to subscript q order, obtain the echo data matrix X of Q pulse:

X＝[x ₁，…，x _Q]＝(A _r*A _ut)B+W

Wherein, B represents the target scattering coefficient matrix of Q subpulse, B=[b ₁..., b _q]; W represents the additive white noise matrix of Q subpulse, W=[n ₁..., n _q].

It should be noted that, microwave relevance imaging radar mockup, refer to that radar receives and emitting antenna is placed in same plane jointly, they are θ relative to the angle of pitch of p target _p, position angle is φ _p.

Step 2, three according to described rectangular arrangement receive the invariable rotary characteristic that array element obtains described echo data matrix, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix according to described invariable rotary characteristic, and according to described first data selection matrix, the second data selection matrix and the 3rd data selection matrix, the element in described echo data matrix is divided into groups respectively, obtain the first corresponding integrated data, the second integrated data and the 3rd integrated data.

The present embodiment, for microwave relevance imaging model, in order to go out the directional information of target from reception extracting data, and then estimates the amplitude phase error of transmitting antenna array, needs construction data selection matrix.The object of design data selection matrix is divided into groups to the element in echo data matrix, forms the invariable rotary factor, and then can extract the directional information of target between the element of difference group.

Step 2 described in the present embodiment comprises following sub-step:

2a) obtain the invariable rotary characteristic in described echo data matrix between element according to three reception array elements of described rectangular arrangement, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix respectively according to described invariable rotary characteristic, wherein the first data selection matrix is:

$J_1=\[1,0,0\]\⊗I_M$

Second data selection matrix is:

$J_2=\[0,1,0\]\⊗I_M$

3rd data selection matrix is:

Wherein, I _mfor the unit matrix of M × M dimension, represent that Kronecker amasss;

2b) described first data selection matrix, the second data selection matrix and the 3rd data selection matrix is utilized to select the element in described echo data matrix X and divide into groups respectively, obtain the first corresponding integrated data, comprise the second integrated data of the invariable rotary factor and comprise the 3rd integrated data of the invariable rotary factor, wherein the first integrated data is:

X ₁＝J ₁X＝A _utB+J ₁W

Second integrated data is: X ₂=J ₂x=A _utΛ _xb+J ₂w

3rd integrated data is:

X ₃＝J ₃X＝A _utΛ _vB+J ₃W

Wherein, for the invariable rotary factor relative to x-axis, ${\mathrm{\Λ}}_y=diag(\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{dcos\φ}}_{y,1}},\mathrm{...},e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{dcos\φ}}_{y,P}}\])$ For the invariable rotary factor relative to y-axis.

It should be noted that, after above-mentioned dimension-reduction treatment is done to data X, just can obtain invariable rotary factor Λ _xand Λ _y, utilize subspace class algorithm just can extract the angle information of target from echo, and the extraction of target angle information is not by the impact of transmitting antenna array amplitude phase error.

Step 3, estimate the Cross-covariance of the Cross-covariance of the auto-covariance matrix of described first integrated data, described first integrated data and the second integrated data, described first integrated data and the 3rd integrated data respectively, sequential combination is data covariance matrix.

SwerlingII type is obeyed according to Target scatter section area, namely target scattering resonance state pulse and interpulse be independently, in conjunction with the ergodic theorem of integrated data, utilize time average to replace average statistical, auto-covariance matrix and the Cross-covariance of integrated data can be estimated, in the present embodiment, auto-covariance matrix and Cross-covariance are referred to as data covariance matrix.

3a) obtain the first integrated data X by following formulae discovery ₁autocorrelation matrix R ₁₁:

$R_{11}=\frac{1}{Q}{X}_1{X_1}^H=A_{ut}{R}_B{A_{ut}}^H+{{\mathrm{\σ}}_n}^2{I}_M$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor having the transmitting antenna array in amplitude phase error situation, σ _n ²for noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix.

It should be noted that, the average statistical that the present invention utilizes time average to replace in described integrated data, obtain integrated data X ₁autocorrelation matrix R ₁₁.

3b) by following formula to the first integrated data X ₁autocorrelation matrix R ₁₁carry out Eigenvalues Decomposition, obtain the estimation of noise power

$R_{11}=U_r{\mathrm{\Λ}}_r{U}_r^H$

${{\widehat{\mathrm{\σ}}}_n}^2=\frac{1}{Q}\underset{k=M-Q+1}{\overset{M}{\Σ}}{\mathrm{\λ}}_{r,k}$

Wherein, the diagonal matrix Λ of proper vector formation _r=diag ([λ _{r, 1}, λ _{r, 2}..., λ _{r, M}]), wherein λ _{r, 1}>=λ _{r, 2}>=...>=λ _{r, M}, U _rfor the matrix that proper vector is formed, operational symbol () ^hthe conjugate transpose of representing matrix, Q indicating impulse number, M represents the element number of array of transmitting antenna array.

3c) by the estimation of noise power from the first integrated data X ₁autocorrelation matrix R ₁₁middle deduction, obtains the first integrated data X ₁auto-covariance matrix R _11s:

$R_{11s}=R_{11}-{{\widehat{\mathrm{\σ}}}_n}^2{I}_M\≈A_{ut}{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, for the estimation of noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix.

3d) obtain the first integrated data X by following formulae discovery ₁with the second integrated data X ₂cross-covariance R ₂₁:

$R_{21}=\frac{1}{Q}{X}_2{X_1}^H=A_{ut}{\mathrm{\Λ}}_x{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to x-axis, operational symbol () ^hthe conjugate transpose of representing matrix.

3e) obtain the first integrated data X by following formulae discovery ₁with the 3rd integrated data X ₃cross-covariance R ₃₁:

$R_{31}=\frac{1}{Q}{X}_3{X_1}^H=A_{ut}{\mathrm{\Λ}}_y{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to y-axis, operational symbol () ^hthe conjugate transpose of representing matrix.

3f) by described first integrated data X ₁auto-covariance matrix R _11s, the first integrated data X ₁with the second integrated data X ₂cross-covariance R ₂₁, the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance R ₃₁sequential combination is data covariance matrix.

Step 4, utilizes described data covariance matrix to carry out angle on target estimation, obtains the direction vector of target.

The present embodiment utilizes invariable rotary factor Λ _xand Λ _ycan extract the space angle information of target, described step 4 comprises following sub-step:

4a) according to following formula pair do svd:

Wherein, R _11sbe the first integrated data X ₁auto-covariance matrix, R ₂₁be the first integrated data X ₁with the second integrated data X ₂cross-covariance, for asking pseudo-inverse operation to accord with, Λ _x=diag ([λ _{x, 1}..., λ _{x, P}]) diagonal matrix that forms for P eigenwert, U _xt=[v _{xt, 1}..., v _{xt, P}] matrix that forms for P eigenwert characteristic of correspondence vector.

4b) according to following formula to be set forth in p eigenvalue λ _{x, p}carry out computing, obtain the cone angle φ of p target relative to x-axis _{x, p}:

${\mathrm{\φ}}_{x,p}=arccos\[\∠\left({\mathrm{\λ}}_{x,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression.

4c) according to following formula pair do svd:

Wherein, R ₃₁be the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance, R _11sbe the first integrated data X ₁auto-covariance matrix, for asking pseudo-inverse operation to accord with, Λ _y=diag ([λ _{y, 1}..., λ _{y, P}]) diagonal matrix that forms for P eigenwert, U _yt=[v _{yt, 1}..., v _{yt, P}] matrix that forms for P eigenwert characteristic of correspondence vector.

4d) according to following formula to described p eigenvalue λ _{y, p}operation, can obtain the cone angle φ of p target relative to y-axis _{y, p}:

${\mathrm{\φ}}_{y,p}=arccos\[\∠\left({\mathrm{\λ}}_{y,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression.

4e) corresponding according to following formulae discovery p target direction vector r _p:

$r_p={\[{\mathrm{cos\φ}}_{x,p},{\mathrm{cos\φ}}_{y,p},\sqrt{1-{\cos }^2{\mathrm{\φ}}_{x,p}-{\cos }^2{\mathrm{\φ}}_{y,p}}\]}^T$

Wherein φ _{x, p}be the cone angle of p target relative to x-axis, φ _{y, p}be the cone angle of p target relative to y-axis.

Step 5, estimates the range error of described transmitting antenna array and phase error respectively according to the direction vector of described target, obtains range error estimated value and the phase error estimation and phase error value of described transmitting antenna array.

It should be noted that, obtain proper vector U according to abovementioned steps _xtwith the direction vector r of target _p, can in conjunction with the position r of transmitting antenna array m array element _{t, m}=[x _m, y _m, 0] ^testimate the amplitude phase error of transmitting antenna array.Described amplitude phase error comprises range error and phase error.

Described step 5 comprises following sub-step:

The transmitting steering vector a (r of p target time 5a) error free according to following formulae discovery _p):

$a\left(r_p\right)={\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,1}}^T{r}_p},\mathrm{...},e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,M}}^T{r}_p}\]}^T$

Wherein, r _{t, 1}..., r _{t, M}represent the 1st to M position of launching array element respectively, operational symbol () ^trepresent transpose operation.

5b) according to following formula to p proper vector v _{xt, p}normalization, obtains described transmitting steering vector a (r _p) estimation

$\hat{a}\left(r_p\right)=v_{xt,p}/v_{xt,p}\left(1\right),p=1,2,...,P$

Wherein, v _{xt, p}(1) v is represented _{xt, p}the value of first element.

The range error estimated value ρ of array element 5c) is launched according to following formulae discovery m _m:

${\mathrm{\ρ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\left|{\hat{a}}_{p,m}\right|}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, operational symbol || for asking absolute value sign.

The phase error estimation and phase error value ψ of array element 5d) is launched according to following formulae discovery m _m:

${\mathrm{\ψ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\∠\left({\hat{a}}_{p,m}{a}_{p,m}^{*}\right)}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, a _{p, m}for launching steering vector a (r _p) m element, operational symbol () ^*represent conjugate operation.

Owing to obtaining the range error ρ of all M of a transmitting antenna array array element _m, m=1,2 ..., M, and phase error ψ _m, m=1,2 ..., M.Therefore by carrying out amplitude phase error compensation to transmission channel, more satisfactory space-time radiation field can be obtained, and then utilize microwave relevance imaging algorithm to recover target scene.

Step 6, according to range error estimated value and the phase error estimation and phase error value of described transmitting antenna array, corrects the amplitude of described transmitting antenna array and phase place respectively.

By compensating for transmitting antenna array amplitude and phase place, amplitude and phase error correction can be carried out to transmitting antenna array, the transmitting antenna array after correcting is utilized to launch multiple waveforms, space-time random radiation field accurately can be formed in space, thus ensure the imaging accuracy of microwave relevance imaging radar.

Effect of the present invention can be further illustrated by following emulation experiment.

One. experimental situation

With reference to Fig. 2, example of the present invention various parameters used are as shown in table 1:

Parameter name	Concrete value
		Carrier frequency	8GHz
Launching antenna array array structure	Uniform surface battle array, array element distance half-wavelength
		Transmitting antenna array array number	9×9
Range error	1dB
		Phase error	20 degree
Signal bandwidth	1GHz
		The distance of search coverage center and center of antenna	850m

Parameter name	Concrete value
		Search coverage size	200m×200m
Target is arranged	9 targets are evenly arranged in search coverage
		Interval between target	X-axis and the equal interval 5m in y-axis direction
Fast umber of beats	1000
		Signal to noise ratio (S/N ratio)	25dB

Table 1 microwave relevance imaging radar parameter is arranged

Two. emulation content and result

Under described simulated conditions, test as follows:

Fig. 3 is the range error comparison diagram of true amplitude error corresponding to 81 array element and estimation, and Fig. 4 is the phase error comparison diagram of true phase error corresponding to 81 array element and estimation.As can be seen from the result of Fig. 3 and Fig. 4, utilize microwave relevance imaging radar amplitude phase error correction method of the present invention accurately can estimate range error and the phase error of microwave relevance imaging radar.

Fig. 5 is the Real profiles of search coverage 9 targets.When Fig. 6 compensates for not carrying out amplitude phase error, utilize the imaging results that microwave relevance imaging algorithm obtains; Fig. 7 is for utilizing this method to estimate amplitude phase error and after compensating amplitude phase error, utilizing the imaging results that microwave relevance imaging algorithm obtains.Comparison diagram 5, Fig. 6 and Fig. 7 can prove validity of the present invention further, namely the present invention On-line Estimation can go out the amplitude phase error of microwave relevance imaging transmitting radar antenna array effectively, and after carrying out amplitude phase error compensation, the imaging performance of microwave relevance imaging radar is restored.

To sum up, but this simulating, verifying correctness of the present invention is linear and reliability.

For aforesaid each embodiment of the method, in order to simple description, therefore it is all expressed as a series of combination of actions, but those skilled in the art should know, the present invention is not by the restriction of described sequence of movement, because according to the present invention, some step can adopt other orders or carry out simultaneously.Secondly, those skilled in the art also should know, the embodiment described in instructions all belongs to preferred embodiment, and involved action and module might not be that the present invention is necessary.

Each embodiment in this instructions all adopts the mode of going forward one by one to describe, and what each embodiment stressed is the difference with other embodiments, between each embodiment identical similar part mutually see.

The present invention can describe in the general context of computer executable instructions, such as program module.Usually, program module comprises the routine, program, object, assembly, data structure etc. that perform particular task or realize particular abstract data type.Also can put into practice the present invention in a distributed computing environment, in these distributed computing environment, be executed the task by the remote processing devices be connected by communication network.In a distributed computing environment, program module can be arranged in the local and remote computer-readable storage medium comprising memory device.

Finally, also it should be noted that, in this article, the such as relational terms of first and second grades and so on is only used for an entity or operation to separate with another entity or operational zone, and not necessarily requires or imply the relation that there is any this reality between these entities or operation or sequentially.And, term " comprises ", " comprising " or its any other variant are intended to contain comprising of nonexcludability, thus make to comprise the process of a series of key element, method, commodity or equipment and not only comprise those key elements, but also comprise other key elements clearly do not listed, or also comprise by the intrinsic key element of this process, method, commodity or equipment.When not more restrictions, the key element limited by statement " comprising ... ", and be not precluded within process, method, commodity or the equipment comprising described key element and also there is other identical element.

Above to a kind of microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element provided by the present invention, be described in detail, apply specific case herein to set forth principle of the present invention and embodiment, the explanation of above embodiment just understands method of the present invention and core concept thereof for helping; Meanwhile, for one of ordinary skill in the art, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.

Claims (6)

1., based on a microwave relevance imaging radar amplitude phase error correction method for auxiliary array element, it is characterized in that, comprise the following steps:

Step 1, the transmitting antenna array of microwave relevance imaging radar launches multiple transmitted waveform, the receiving antenna array of described microwave relevance imaging radar receives corresponding multiple echo data, matched filtering is carried out to described echo data, and order arrangement is carried out to filtered echo data, obtain echo data matrix; Wherein, described receiving antenna array comprises three reception array elements of at right angles arrangement;

Step 2, three according to described rectangular arrangement receive the invariable rotary characteristic that array element obtains described echo data matrix, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix according to described invariable rotary characteristic, and according to described first data selection matrix, the second data selection matrix and the 3rd data selection matrix, the element in described echo data matrix is divided into groups respectively, obtain the first corresponding integrated data, the second integrated data and the 3rd integrated data;

Step 3, estimate the Cross-covariance of the Cross-covariance of the auto-covariance matrix of described first integrated data, described first integrated data and the second integrated data, described first integrated data and the 3rd integrated data respectively, sequential combination is data covariance matrix;

Step 4, utilizes described data covariance matrix to carry out angle on target estimation, obtains the direction vector of target;

Step 5, estimates the range error of described transmitting antenna array and phase error respectively according to the direction vector of described target, obtains range error estimated value and the phase error estimation and phase error value of described transmitting antenna array;

Step 6, according to range error estimated value and the phase error estimation and phase error value of described transmitting antenna array, corrects the amplitude of described transmitting antenna array and phase place respectively.

2. the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element according to claim 1, it is characterized in that, described step 1 comprises following sub-step:

1a) transmitting antenna array of microwave relevance imaging radar comprises M transmitting array element, launches array element for described M and launches multiple transmitted waveform, and m the complex envelope launching the transmitted waveform of array element is s _m, wherein M is natural number, and m is natural number, and m=1 ..., M;

1b) receiving antenna array of microwave relevance imaging radar comprises N number of reception array element, and described N number of reception array element receives corresponding multiple echo data, and the n-th echo data receiving the q subpulse that array element receives is y _n,q, wherein N is natural number, and n is natural number, and n=1 ..., N, N=3;

Echo data and described M the conjugation of launching the complex envelope of the transmitted waveform of array element of q subpulse 1c) described N number of reception array element received make inner product, obtain corresponding matched filtering and export x _q, wherein x _q(n-1) M+m element be represent the echo data y receiving the q subpulse that array element receives by described n-th _n,qthe complex envelope s of the transmitted waveform of array element is launched with m _mconjugation make inner product after, obtain corresponding matched filtering and export, obtained by following formulae discovery:

Wherein, n=1 ..., N; M=1 ..., M; Q=1 ..., Q, Q indicating impulse number of times, M, m, N, n, Q, q are natural number;

1d) matched filtering corresponding for described N number of reception array element output is lined up a column vector according to subscript m and subscript n order successively, obtain the matched filtering result x of q subpulse _q;

Receive array element by n-th and according to subscript m order, a column vector is lined up for the matched filtering Output rusults that M is launched the complex envelope of the transmitted waveform of array element

Will a column vector x is lined up according to subscript n order _q:

Wherein, operational symbol () ^trepresent transpose operation, sign of operation * represents that Khatri-Rao amasss, n _qfor additive white Gaussian noise, b _qfor obeying the target complex scattering coefficients of SwerlingII type, A _rfor receiving antenna array steering vector, A _utfor there being the transmitting antenna array steering vector in amplitude phase error situation;

Described matched filtering result x 1e) Q pulse obtained respectively _qline up a matrix according to subscript q order, obtain the echo data matrix X of Q pulse:

X＝[x ₁,...,x _Q]＝(A _r*A _ut)B+W

Wherein, B represents the target scattering coefficient matrix of Q subpulse, B=[b ₁..., b _q]; W represents the additive white noise matrix of Q subpulse, W=[n ₁..., n _q].

3. the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element according to claim 1, it is characterized in that, described step 2 comprises following sub-step:

2a) obtain the invariable rotary characteristic in described echo data matrix between element according to three reception array elements of described rectangular arrangement, and construct the first data selection matrix, the second data selection matrix and the 3rd data selection matrix respectively according to described invariable rotary characteristic, wherein the first data selection matrix is:

$J_1=\left[\mathrm{1,0,0}\right]\⊗I_M$

Second data selection matrix is:

$J_2=\left[\mathrm{0,1,0}\right]\⊗I_M$

3rd data selection matrix is: $J_3=\left[\mathrm{0,0,1}\right]\⊗I_M$

Wherein, I _mfor the unit matrix of M × M dimension, represent that Kronecker amasss;

2b) described first data selection matrix, the second data selection matrix and the 3rd data selection matrix is utilized to select the element in described echo data matrix X and divide into groups respectively, obtain the first corresponding integrated data, comprise the second integrated data of the invariable rotary factor and comprise the 3rd integrated data of the invariable rotary factor, wherein the first integrated data is:

X ₁＝J ₁X＝A _utB+J ₁W

Second integrated data is: X ₂=J ₂x=A _utΛ _xb+J ₂w

3rd integrated data is:

X ₃＝J ₃X＝A _utΛ _yB+J ₃W

Wherein, for the invariable rotary factor relative to x-axis, ${\mathrm{\Λ}}_y=diag(\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}d{\mathrm{cos\φ}}_{y,1}},...,e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}d{\mathrm{cos\φ}}_{y,P}}\])$ For the invariable rotary factor relative to y-axis.

4. the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element according to claim 1, it is characterized in that, described step 3 comprises following sub-step:

3a) obtain the first integrated data X by following formulae discovery ₁autocorrelation matrix R ₁₁:

$R_{11}=\frac{1}{Q}{X}_1{X_1}^H=A_{ut}{R}_B{A_{ut}}^H+{{\mathrm{\σ}}_n}^2{I}_M$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor having the transmitting antenna array in amplitude phase error situation, σ _n ²for noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix;

3b) by following formula to the first integrated data X ₁autocorrelation matrix R ₁₁carry out Eigenvalues Decomposition, obtain the estimation of noise power

$R_{11}=U_r{\mathrm{\Λ}}_r{U}_r^H$

${{\widehat{\mathrm{\σ}}}_n}^2=\frac{1}{Q}\underset{k=M-Q+1}{\overset{M}{\Σ}}{\mathrm{\λ}}_{r,k}$

Wherein, the diagonal matrix Λ of proper vector formation _r=diag ([λ _{r, 1}, λ _{r, 2}..., λ _r,M]), wherein λ _{r, 1}>=λ _{r, 2}>=...>=λ _r,M, U _rfor the matrix that proper vector is formed, operational symbol () ^hthe conjugate transpose of representing matrix, Q indicating impulse number, M represents the element number of array of transmitting antenna array;

3c) by the estimation of noise power from the first integrated data X ₁autocorrelation matrix R ₁₁middle deduction, obtains the first integrated data X ₁auto-covariance matrix R _11s:

$R_{11s}=R_{11}-{{\widehat{\mathrm{\σ}}}_n}^2{I}_M\≈A_{ut}{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, for the estimation of noise power, Q indicating impulse number, I _mrepresent the unit matrix of M × M, operational symbol () ^hthe conjugate transpose of representing matrix;

3d) obtain the first integrated data X by following formulae discovery ₁with the second integrated data X ₂cross-covariance R ₂₁:

$R_{21}=\frac{1}{Q}{X}_2{X_1}^H=A_{ut}{\mathrm{\Λ}}_x{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to x-axis, operational symbol () ^hthe conjugate transpose of representing matrix;

3e) obtain the first integrated data X by following formulae discovery ₁with the 3rd integrated data X ₃cross-covariance R ₃₁:

$R_{31}=\frac{1}{Q}{X}_3{X_1}^H=A_{ut}{\mathrm{\Λ}}_y{R}_B{A_{ut}}^H$

Wherein, b represents the target scattering coefficient matrix of Q subpulse, A _utfor there being the transmitting antenna array in amplitude phase error situation, Q indicating impulse number, for the invariable rotary factor relative to y-axis, operational symbol () ^hthe conjugate transpose of representing matrix;

3f) by described first integrated data X ₁auto-covariance matrix R _11s, the first integrated data X ₁with the second integrated data X ₂cross-covariance R ₂₁, the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance R ₃₁sequential combination is data covariance matrix.

5. the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element according to claim 1, it is characterized in that, described step 4 comprises following sub-step:

4a) according to following formula pair do svd:

Wherein, R _11sbe the first integrated data X ₁auto-covariance matrix, R ₂₁be the first integrated data X ₁with the second integrated data X ₂cross-covariance, for asking pseudo-inverse operation to accord with, Λ _x=diag ([λ _{x, 1}..., λ _x,P]) diagonal matrix that forms for P eigenwert, U _xt=[v _{xt, 1}..., v _{xt, P}] matrix that forms for P eigenwert characteristic of correspondence vector;

4b) according to following formula to be set forth in p eigenvalue λ _x,pcarry out computing, obtain the cone angle φ of p target relative to x-axis _x,p:

${\mathrm{\φ}}_{x,p}=arccos\[\∠\left({\mathrm{\λ}}_{x,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression;

4c) according to following formula pair do svd:

Wherein, R ₃₁be the first integrated data X ₁with the 3rd integrated data X ₃cross-covariance, R _11sbe the first integrated data X ₁auto-covariance matrix, for asking pseudo-inverse operation to accord with, Λ _y=diag ([λ _{y, 1}..., λ _y,P]) diagonal matrix that forms for P eigenwert, U _yt=[v _{yt, 1}..., v _{yt, P}] matrix that forms for P eigenwert characteristic of correspondence vector;

4d) according to following formula to described p eigenvalue λ _y,poperation, can obtain the cone angle φ of p target relative to y-axis _y,p:

${\mathrm{\φ}}_{y,p}=arccos\[\∠\left({\mathrm{\λ}}_{y,p}\right)\frac{\mathrm{\λ}}{2\mathrm{\π}d}\]$

Wherein, the computing of multiple angle is got in operational symbol ∠ () expression;

4e) corresponding according to following formulae discovery p target direction vector r _p:

$r_p={\[{\mathrm{cos\φ}}_{x,p},{\mathrm{cos\φ}}_{y,p},\sqrt{1-{\cos }^2{\mathrm{\φ}}_{x,p}-{\cos }^2{\mathrm{\φ}}_{y,p}}\]}^T$

Wherein φ _x,pbe the cone angle of p target relative to x-axis, φ _y,pbe the cone angle of p target relative to y-axis.

6. the microwave relevance imaging radar amplitude phase error correction method based on auxiliary array element according to claim 1, it is characterized in that, described step 5 comprises following sub-step:

The transmitting steering vector a (r of p target time 5a) error free according to following formulae discovery _p):

$a\left(r_p\right)={\[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,1}}^T{r}_p},...,e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}{r_{t,M}}^T{r}_p}\]}^T$

Wherein, r _{t, 1}..., r _t,Mrepresent the 1st to M position of launching array element respectively, operational symbol () ^trepresent transpose operation;

5b) according to following formula to p proper vector v _{xt, p}normalization, obtains described transmitting steering vector a (r _p) estimation

$\hat{a}\left(r_p\right)=v_{xt,p}/v_{xt,p}\left(1\right),p=1,2,...,P$

Wherein, v _{xt, p}(1) v is represented _{xt, p}the value of first element;

The range error estimated value ρ of array element 5c) is launched according to following formulae discovery m _m:

${\mathrm{\ρ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\left|{\hat{a}}_{p,m}\right|}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, operational symbol || for asking absolute value sign;

The phase error estimation and phase error value ψ of array element 5d) is launched according to following formulae discovery m _m:

${\mathrm{\ψ}}_m=\frac{\underset{p=1}{\overset{P}{\Σ}}\∠\left({\hat{a}}_{p,m}{a}_{p,m}^{*}\right)}{P},m=1,2,...,M$

Wherein, for launching steering vector a (r _p) estimation m element, a _p,mfor launching steering vector a (r _p) m element, operational symbol () ^*represent conjugate operation.