CN105044693B - Microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element - Google Patents

Microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element Download PDF

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CN105044693B
CN105044693B CN201510359715.0A CN201510359715A CN105044693B CN 105044693 B CN105044693 B CN 105044693B CN 201510359715 A CN201510359715 A CN 201510359715A CN 105044693 B CN105044693 B CN 105044693B
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CN105044693A (en
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李军
朱圣棋
郑煜
李小敏
廖桂生
赵启勇
马玉芳
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating

Abstract

A kind of microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element of offer of the present invention, to estimate the amplitude phase error of microwave relevance imaging radar, and then obtains ideal space-time radiation field by being compensated to amplitude phase error.Including：Step 1：The transmitting antenna array transmitting multiple waveforms of microwave relevance imaging radar, receiving antenna array receives corresponding a variety of echo datas, and matched filtering is carried out to echo data, and order arranges and obtains echo data matrix；Step 2：Element in echo data matrix is grouped；Step 3：Estimated data covariance matrix；Step 4：Angle on target estimation is carried out, the direction vector of target is obtained；Step 5：The range error and phase error of transmitting antenna array are estimated respectively, corresponding error estimate is obtained；Step 6, according to the range error estimate and phase error estimation and phase error value of transmitting antenna array, the amplitude and phase to transmitting antenna array are corrected respectively.

Description

Microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element
Technical field
The invention belongs to Radar Technology field, more particularly to a kind of microwave relevance imaging radar amplitude phase based on auxiliary array element Error calibration method, the on line emendation applied to relevance imaging radar array amplitude phase error.
Background technology
Radar is essential electronics in the modern life, and wherein microwave relevance imaging radar system can be realized pair In the staring imaging of scene, there is wide application prospect in scenes such as national defence, anti-terrorism, securities.Due to microwave relevance imaging radar Need to launch different signals in different transmitting array elements, therefore the larger amplitude phase error of introducing be easier than traditional array radar, Simultaneously amplitude phase error can over time, the environmental factor such as temperature is continually changing.When there is amplitude phase error, microwave relevance imaging thunder The space-time radiation field reached can be distorted, and this can cause the decline of microwave relevance imaging radar imagery performance even can not be into Picture.Due to radar amplitude phase error over time, the environmental factor such as temperature be continually changing, therefore effectively On-line Estimation width is mutually missed Difference is a key issue of microwave relevance imaging radar application.
The patent " microwave relevance imaging system and imaging method based on thinned array " of Xian Electronics Science and Technology University's application Microwave relevance imaging system and imaging method based on thinned array are disclosed in (application number 201310167360.6).This method Relevance imaging theory is extended to microwave regime from optics, and utilizes the problem of compressive sensing theory solves corresponding, is realized super Cross the imaging effect of Rayleigh diffraction limit.But, the defect of this method is the amplitude phase error for not accounting for array, when radar battle array When row have amplitude phase error, the transmission signal of radar can be influenceed by amplitude phase error, thus the space-time synthesized in space is random There is certain error in radiation field, this decline for eventually resulting in imaging performance is even imaged relative to preferable space-time radiation field Fall flat.
Current radar array correction is main to be corrected technology using calibration source, can more accurately estimate in these sides Count out the amplitude phase error of array.In many practical application scenes, due to radar array amplitude phase error can over time, temperature etc. Environmental factor is continually changing, it is necessary to be corrected online to amplitude phase error, being corrected using calibration source just has great limitation Property.
The content of the invention
For above-mentioned technical problem, it is an object of the invention to provide a kind of microwave relevance imaging thunder based on auxiliary array element Up to amplitude and phase error correction method, to estimate the amplitude phase error of microwave relevance imaging radar, and then by being mended to amplitude phase error Repay and obtain ideal space-time radiation field, it is final to utilize relevance imaging algorithm reconstruct image scene.
In order to achieve the above object, the present invention is achieved using following technical scheme.
A kind of microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element, comprises the following steps：
Step 1, the transmitting antenna array of microwave relevance imaging radar launches a variety of transmitted waveforms, the microwave relevance imaging The receiving antenna array of radar receives corresponding a variety of echo datas, and matched filtering is carried out to the echo data, and to filtering Echo data carry out order arrangement afterwards, obtains echo data matrix；Wherein, the receiving antenna array includes rectangular arrangement Three reception array elements；
Step 2, the invariable rotary that array element obtains the echo data matrix is received according to three at right angles arranged Characteristic, and the first data selection matrix, the second data selection matrix and the choosing of the 3rd data are constructed according to the invariable rotary characteristic Matrix is selected, and respectively according to the first data selection matrix, the second data selection matrix and the 3rd data selection matrix to institute The element stated in echo data matrix is grouped, and obtains corresponding first grouped data, second packet data and the 3rd packet Data；
Step 3, the auto-covariance matrix of first grouped data, first grouped data and second point are estimated respectively Cross-covariance, the Cross-covariance of first grouped data and the 3rd grouped data of data are organized, sequential combination is Data covariance matrix；
Step 4, angle on target estimation is carried out using the data covariance matrix, obtains the direction vector of target；
Step 5, missed according to the direction vector of target range error respectively to the transmitting antenna array and phase Difference is estimated, obtains the range error estimate and phase error estimation and phase error value of the transmitting antenna array；
Step 6, according to the range error estimate and phase error estimation and phase error value of the transmitting antenna array, respectively to described The amplitude and phase of transmitting antenna array are corrected.
Preferably, the step 1 includes following sub-step：
1a) transmitting antenna array of microwave relevance imaging radar includes M transmitting array element, the M transmitting array element transmitting A variety of transmitted waveforms, the complex envelope of the transmitted waveform of m-th of transmitting array element is sm, wherein M is natural number, and m is natural number, and m =1 ..., M；
1b) receiving antenna array of microwave relevance imaging radar includes N number of reception array element, and N number of reception array element is received Corresponding a variety of echo datas, the echo data for the q subpulses that n-th of reception array element is received is yN, q, wherein N is nature Number, n is natural number, and n=1 ..., N, N=3；
1c) by N number of echo data for receiving the q subpulses that array element is received and the hair of described M transmitting array element The conjugation of the complex envelope of ejected wave shape makees inner product, obtains corresponding matched filtering output xq, wherein xq(n-1) M+m element beRepresent the echo data y of q subpulses for receiving described n-th reception array elementN, qWith m-th of transmitting battle array The complex envelope s of the transmitted waveform of membermConjugation make after inner product, obtain corresponding matched filtering output,Pass through below equation Calculating is obtained：
Wherein, n=1 ..., N；M=1 ..., M；Q=1 ..., Q, Q represent pulse number, and M, m, N, n, Q, q are nature Number；
N number of reception array element corresponding matched filtering output 1d) is lined up one according to subscript m and subscript n order successively Individual column vector, obtains the matched filtering result x of q subpulsesq；
Array element is received by n-th to press for the matched filtering output result of the complex envelope of the transmitted waveform of M transmitting array element A column vector is lined up according to subscript m order
WillA column vector x is lined up according to subscript n orderq：
Wherein, operator ()TTransposition computing is represented, oeprator * represents that Khatri-Rao is accumulated, nqFor additive white gaussian Noise, bqTo obey the target complex scattering coefficients of Swerling II types, ArFor receiving antenna array steering vector, AutTo there is width Transmitting antenna array steering vector under phase error condition；
1e) the matched filtering result x for respectively obtaining Q pulseqA matrix is lined up according to subscript q orders, is obtained To the echo data matrix X of Q pulse：
X=[x1..., xQ]=(Ar*Aut)B+W
Wherein, B represents the target scattering coefficient matrix of Q subpulses, B=[b1..., bQ]；W represents the additive white of Q subpulses Noise matrix, W=[n1 ..., nQ]。
Preferably, the step 2 includes following sub-step：
The rotation in the echo data matrix between element 2a) is obtained according to the three reception array elements at right angles arranged Turn invariant feature, and according to the invariable rotary characteristic construct respectively the first data selection matrix, the second data selection matrix and 3rd data selection matrix, wherein the first data selection matrix is：
Second data selection matrix is：
3rd data selection matrix is：
Wherein, IMThe unit matrix tieed up for M × M,Represent Kronecker products；
It is 2b) right respectively using the first data selection matrix, the second data selection matrix and the 3rd data selection matrix Element in the echo data matrix X is selected and is grouped, obtain corresponding first grouped data, comprising invariable rotary because The second packet data of son and the 3rd grouped data comprising the invariable rotary factor, wherein the first grouped data is：
X1=J1X=AutB+J1W
Second packet data are：X2=J2X=AutΛxB+J2W
3rd grouped data is：
X3=J3X=AutΛyB+J3W
Wherein,For the invariable rotary factor relative to x-axis,For the invariable rotary factor relative to y-axis.
Preferably, the step 3 includes following sub-step：
3a) calculated by below equation and obtain the first grouped data X1Autocorrelation matrix R11：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, σn 2For noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator ()HTable Show the conjugate transposition of matrix；
3b) by below equation to the first grouped data X1Autocorrelation matrix R11Eigenvalues Decomposition is carried out, noise is obtained The estimation of power
Wherein, the diagonal matrix Λ that characteristic vector is constitutedr=diag ([λR, 1, λR, 2..., λR, M]), wherein λR, 1≥λR, 2 ≥…≥λR, M, UrIt is characterized the matrix of vector composition, operator ()HThe conjugate transposition of representing matrix, Q represents pulse number, M Represent the element number of array of transmitting antenna array；
3c) by the estimation of noise powerFrom the first grouped data X1Autocorrelation matrix R11It is middle to deduct, obtain first point Group data X1Auto-covariance matrix R11s：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array,For the estimation of noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator (·)HThe conjugate transposition of representing matrix；
3d) calculated by below equation and obtain the first grouped data X1With second packet data X2Cross-covariance R21：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, Q represents pulse number,For the rotation relative to x-axis Invariant factor, operator ()HThe conjugate transposition of representing matrix；
3e) calculated by below equation and obtain the first grouped data X1With the 3rd grouped data X3Cross-covariance R31：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, Q represents pulse number,For the rotation relative to y-axis Invariant factor, operator ()HThe conjugate transposition of representing matrix；
3f) by the first grouped data X1Auto-covariance matrix R11s, the first grouped data X1With second packet data X2Cross-covariance R21, the first grouped data X1With the 3rd grouped data X3Cross-covariance R31Sequential combination is number According to covariance matrix.
Preferably, the step 4 includes following sub-step：
4a) according to below equation pairDo singular value decomposition：
Wherein, R11sFor the first grouped data X1Auto-covariance matrix, R21For the first grouped data X1With second packet number According to X2Cross-covariance,To ask pseudo-inverse operation to accord with, Λx=diag ([λX, 1..., λX, P]) constituted for P characteristic value Diagonal matrix, Uxt=[vXt, 1... vXt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted；
4b) according to below equation to being set forth in p-th of eigenvalue λX, pComputing is carried out, p-th of target is obtained relative to x-axis Cone angle φX, p：
Wherein, operator ∠ () represents to take multiple angle computing；
4c) according to below equation pairDo singular value decomposition：
Wherein, R31For the first grouped data X1With the 3rd grouped data X3Cross-covariance, R11sFor the first packet count According to X1Auto-covariance matrix,To ask pseudo-inverse operation to accord with, Λy=diag ([λY, 1..., λY, P]) constituted for P characteristic value Diagonal matrix, Uyt=[vYt, 1..., vYt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted；
4d) according to below equation to p-th of eigenvalue λY, pOperation, can obtain p-th of target relative to y-axis Cone angle φY, p：
Wherein, operator ∠ () represents to take multiple angle computing；
The corresponding direction vector r of p-th of target 4e) is calculated according to below equationp：
Wherein φX, pCone angle for p-th of target relative to x-axis, φY, pCone angle for p-th of target relative to y-axis.
Preferably, the step 5 includes following sub-step：
The transmitting steering vector a (r of p-th of target when 5a) calculating error free according to below equationp)：
Wherein, rT, 1..., rT, MThe 1st position for launching array element to m-th, operator () are represented respectivelyTRepresent transposition Computing；
5b) according to below equation to p-th of characteristic vector vXt, pNormalization, obtains the transmitting steering vector a (rp) estimate Meter
Wherein, vXt, p(1) v is representedXt, pFirst element value；
The range error estimate ρ of m-th of transmitting array element 5c) is calculated according to below equationm：
Wherein,For transmitting steering vector a (rp) estimationM-th of element, operator | | to ask absolute It is worth symbol；
The phase error estimation and phase error value ψ of m-th of transmitting array element 5d) is calculated according to below equationm：
Wherein,For transmitting steering vector a (rp) estimationM-th of element, aP, mFor transmitting steering vector a (rp) m-th of element, operator ()*Represent conjugate operation.
The present invention compared with prior art, with advantages below：
First, present invention utilizes each array element transmitting unlike signal of the transmitting antenna array of microwave relevance imaging radar Feature, by auxiliary array element (three reception array element), three groups of data are obtained in receiving terminal matched filtering, and between three groups of data With invariable rotary characteristic, the present invention utilizes invariable rotary characteristic from the direction vector of extraction target, and further estimates The amplitude phase error of microwave relevance imaging radar, then carries out amplitude and phase error correction according to the amplitude phase error that estimation is obtained, it is clear that this Invention does not need calibration source to participate in that radar array can be carried out amplitude and phase error correction, therefore implements simple, and complexity is low, so that The efficiency of microwave relevance imaging radar amplitude and phase error correction can be improved.
Second, the present invention has obtained the direction vector of target in step 4, therefore the present invention is realizing amplitude and phase error correction While can also realize the positioning for target.
3rd, the present invention directly estimates amplitude phase error, therefore the present invention can enter to amplitude phase error from echo data Row on-line correction, i.e., just can carry out amplitude and phase error correction, it is ensured that microwave relevance imaging under radar working condition to radar The real-time of radar amplitude and phase error correction.
4th, the present invention is compensated using the amplitude phase error estimated to transmitting antenna array amplitude and phase, can Amplitude and phase error correction is carried out to transmitting antenna array, multiple waveforms are launched using the transmitting antenna array after correction, can be in sky Between in form accurate space-time random radiation, so as to ensure the imaging accuracy of microwave relevance imaging radar.
Brief description of the drawings
Fig. 1 is a kind of microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element of the embodiment of the present invention Flow chart；
Fig. 2 is the schematic diagram of the geometric configuration of microwave relevance imaging radar used in the present invention；
Fig. 3 is the range error and actual margin error that 81 transmitting array elements of transmitting antenna array are estimated by the present invention Comparison diagram；
Fig. 4 is the phase error and substantial phase error that 81 transmitting array elements of transmitting antenna array are estimated by the present invention Comparison diagram；
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, the target for utilizing microwave relevance imaging algorithm to recover Scene；
During the fast umber of beats 1000 of Fig. 7, carried out using the inventive method after amplitude and phase error correction, recycle microwave relevance imaging to calculate The target scene that method is recovered.
Embodiment
In order to facilitate the understanding of the purposes, features and advantages of the present invention, it is below in conjunction with the accompanying drawings and specific real Applying mode, the present invention is further detailed explanation.
In order to which preferably the present invention will be described, the geometric configuration first to microwave relevance imaging radar used in the present invention Illustrate.Reference picture 2, is the schematic diagram of the geometric configuration of microwave relevance imaging radar used in the present invention, and the present invention is based on micro- The radar system of ripple relevance imaging, including：Array element 1 is received, array element 2 is received, receives array element 3, transmitting antenna array 4, the and of target 5 Signal processor 6.Array element 1 is wherein received, array element 2 is received and receives array element 3 and is referred to as aiding in array element.Produced using transmitting antenna 4 Raw microwave radiation field is irradiated generation echo to target 5, and auxiliary array element receives the echo-signal of target, signal processor 6 The amplitude phase error that echo-signal obtains transmitting antenna array 1 is handled, signal processor 6 is according to obtained amplitude phase error and transmitting day The transmission signal of linear array 4 calculates space-time random radiation, signal processor 6 using calculating space-time random radiation and connect The reception signal transacting for receiving array element 1 obtains the imaging of target.It should be noted that above-mentioned reception array element is also referred to as reception antenna.
The reception array element 1, reception array element 2, reception array element 3 and transmitting antenna array 4 are co-located in same single base thunder Up on platform, a face battle array is collectively formed.
The auxiliary array element, i.e. reception array element 1, reception array element 2 and reception array element 3, they at right angles arrange, i.e., with reception Array element 1 is that origin sets up rectangular coordinate system, receives array element 2 and is distributed in x-axis positive axis, receives array element 3 and is distributed in y-axis positive axis On.The spacing d for receiving array element 1 and receiving the spacing between array element 2 and receiving array element 1 and receive between array element 3 is satisfied byWherein λ is the wavelength of carrier wave.Auxiliary array element be special antenna, its magnitude-phase characteristics, it is known that and substantially not with environment because Element changes.
In Fig. 2, coordinate origin O is set to receive the position of array element 1, receives array element 2 in x-axis positive axis, receives battle array Member 3 is in y-axis positive axis.The azimuth of p-th of target is θp, the angle of pitch is φp, the cone angle relative to x-axis is φX, p, relatively In y-axis cone angle be φY, p, wherein (cos φp)2+(cosφX, p)2+(cosφY, p)2=1.Transmitting antenna array is launched for m-th The positional representation of antenna is rT, m=[xm, ym, 0]T, wherein m=1,2 ... M.
Based on the foregoing explanation to the geometric configuration of microwave relevance imaging radar used in the present invention, with reference to Fig. 1 to this The microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element of invention is illustrated.It is described to be based on auxiliary array element Microwave relevance imaging radar amplitude and phase error correction method can be in fig. 2 signal processor in realize.
Reference picture 1, shows a kind of microwave relevance imaging radar amplitude phase error based on auxiliary array element of the embodiment of the present invention The flow chart of bearing calibration, the present embodiment specifically may comprise steps of：
Step 1, the transmitting antenna array of microwave relevance imaging radar launches a variety of transmitted waveforms, the microwave relevance imaging The receiving antenna array of radar receives corresponding a variety of echo datas, and matched filtering is carried out to the echo data, and to filtering Echo data carry out order arrangement afterwards, obtains echo data matrix；Wherein, the receiving antenna array includes rectangular arrangement Three reception array elements.
The step 1 includes following sub-step：
1a) transmitting antenna array of microwave relevance imaging radar includes M transmitting array element, the M transmitting array element transmitting A variety of transmitted waveforms, the complex envelope of the transmitted waveform of m-th of transmitting array element is sm, wherein M is natural number, and m is natural number, and m =1 ..., M.
It should be noted that the transmitting antenna array 4 described in this step in each transmitting antenna array array element corresponding diagram 2 is wrapped The transmitting antenna array array element contained.
1b) receiving antenna array of microwave relevance imaging radar includes N number of reception array element, and N number of reception array element is received Corresponding a variety of echo datas, the echo data for the q subpulses that n-th of reception array element is received is yN, q, wherein N is nature Number, n is natural number, and n=1 ..., N, N=3.
According to Fig. 2, N takes 3, i.e. microwave relevance imaging radar to include receiving array element 1, receive array element 2 and connect in the present embodiment Array element 3 is received, and 3 receive array element and at right angles arrange, i.e., set up rectangular coordinate system for origin to receive array element 1, receive 2 points of array element Cloth receives array element 3 and is distributed in y-axis positive axis in x-axis positive axis.Receive array element 1 and receive array element 2 between spacing and The spacing d for receiving array element 1 and receiving between array element 3 is satisfied byWherein λ is the wavelength of carrier wave.
According to Fig. 2, using microwave relevance imaging radar mockup, each array element of transmitting antenna array 4 launches different ripples Shape, the echo data for the q subpulses that n-th of reception array element is received is designated as yN, q。
1c) by N number of echo data for receiving the q subpulses that array element is received and the hair of described M transmitting array element The conjugation of the complex envelope of ejected wave shape makees inner product, obtains corresponding matched filtering output xq, wherein xq(n-1) M+m element beRepresent the echo data y of q subpulses for receiving described n-th reception array elementN, qWith m-th of transmitting battle array The complex envelope s of the transmitted waveform of membermConjugation make after inner product, obtain corresponding matched filtering output,Pass through below equation Calculating is obtained：
Wherein, n=1 ..., N；M=1 ..., M；Q=1 ..., Q, Q represent pulse number, and M, m, N, n, Q, q are nature Number.
N number of reception array element corresponding matched filtering output 1d) is lined up one according to subscript m and subscript n order successively Individual column vector, obtains the matched filtering result x of q subpulsesq；
Array element is received by n-th to press for the matched filtering output result of the complex envelope of the transmitted waveform of M transmitting array element A column vector is lined up according to subscript m order
WillA column vector x is lined up according to subscript n orderq：
Wherein, operator ()TTransposition computing is represented, oeprator * represents that Khatri-Rao is accumulated, nqFor additive white gaussian Noise, bqTo obey the target complex scattering coefficients of Swerling II types, ArFor receiving antenna array steering vector, AutTo there is width Transmitting antenna array steering vector under phase error condition.
It should be noted that the present embodiment and the transmitted waveform complex envelope s of m-th of transmitting antenna array array elementmConjugation Make inner product and carry out matched filtering, i.e.,By yN, qWith the number of echoes after all M transmitted waveform matched filterings According to lining up a column vector, you can obtain receiving array element n matched filtering resultFurther according to the matching filter of 3 reception array element Ripple result, which joins end to end, obtains the matched filtering result x of q subpulsesq。
1e) the matched filtering result x for respectively obtaining Q pulseqA matrix is lined up according to subscript q orders, is obtained To the echo data matrix X of Q pulse：
X=[x1..., xQ]=(Ar*Aut)B+W
Wherein, B represents the target scattering coefficient matrix of Q subpulses, B=[b1..., bQ]；W represents the additive white of Q subpulses Noise matrix, W=[n1..., nQ]。
It should be noted that microwave relevance imaging radar mockup, refers to that radar is received and transmitting antenna is placed on together jointly In one plane, they are θ relative to the angle of pitch of p-th of targetp, azimuth is φp。
Step 2, the invariable rotary that array element obtains the echo data matrix is received according to three at right angles arranged Characteristic, and the first data selection matrix, the second data selection matrix and the choosing of the 3rd data are constructed according to the invariable rotary characteristic Matrix is selected, and respectively according to the first data selection matrix, the second data selection matrix and the 3rd data selection matrix to institute The element stated in echo data matrix is grouped, and obtains corresponding first grouped data, second packet data and the 3rd packet Data.
The present embodiment is directed to microwave relevance imaging model, in order to go out the directional information of target from reception extracting data, enters And the amplitude phase error of transmitting antenna array is estimated, it is necessary to construct data selection matrix.The purpose of design data selection matrix is Element in echo data matrix is grouped, the invariable rotary factor is formed between different groups of element, and then can extract Go out the directional information of target.
Step 2 described in the present embodiment includes following sub-step：
The rotation in the echo data matrix between element 2a) is obtained according to the three reception array elements at right angles arranged Turn invariant feature, and according to the invariable rotary characteristic construct respectively the first data selection matrix, the second data selection matrix and 3rd data selection matrix, wherein the first data selection matrix is：
Second data selection matrix is：
3rd data selection matrix is：
Wherein, IMThe unit matrix tieed up for M × M,Represent Kronecker products；
It is 2b) right respectively using the first data selection matrix, the second data selection matrix and the 3rd data selection matrix Element in the echo data matrix X is selected and is grouped, obtain corresponding first grouped data, comprising invariable rotary because The second packet data of son and the 3rd grouped data comprising the invariable rotary factor, wherein the first grouped data is：
X1=J1X=AutB+J1W
Second packet data are：X2=J2X=AutΛxB+J2W
3rd grouped data is：
X3=J3X=AutΛvB+J3W
Wherein,For the invariable rotary factor relative to x-axis,For the invariable rotary factor relative to y-axis.
It should be noted that being done to data X after above-mentioned dimension-reduction treatment, invariable rotary factor Λ just can be obtainedxAnd Λy, profit The angle information of target just can be extracted from echo with subspace class algorithm, and the extraction of target angle information is not sent out Penetrate the influence of aerial array amplitude phase error.
Step 3, the auto-covariance matrix of first grouped data, first grouped data and second point are estimated respectively Cross-covariance, the Cross-covariance of first grouped data and the 3rd grouped data of data are organized, sequential combination is Data covariance matrix.
Swerling II types are obeyed according to Target scatter section area, i.e., the scattering resonance state of target is between pulse and pulse It is independent, with reference to the ergodic theorem of grouped data, average statistical is replaced using time average, it is estimated that packet count According to auto-covariance matrix and Cross-covariance, auto-covariance matrix and Cross-covariance are referred to as number in the present embodiment According to covariance matrix.
3a) calculated by below equation and obtain the first grouped data X1Autocorrelation matrix R11：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, σn 2For noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator ()HTable Show the conjugate transposition of matrix.
It should be noted that the present invention replaces the average statistical in the grouped data using time average, it is grouped Data X1Autocorrelation matrix R11。
3b) by below equation to the first grouped data X1Autocorrelation matrix R11Eigenvalues Decomposition is carried out, noise is obtained The estimation of power
Wherein, the diagonal matrix Λ that characteristic vector is constitutedr=diag ([λR, 1, λR, 2..., λR, M]), wherein λR, 1≥λR, 2 ≥…≥λR, M, UrIt is characterized the matrix of vector composition, operator ()HThe conjugate transposition of representing matrix, Q represents pulse number, M Represent the element number of array of transmitting antenna array.
3c) by the estimation of noise powerFrom the first grouped data X1Autocorrelation matrix R11It is middle to deduct, obtain first point Group data X1Auto-covariance matrix R11s：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array,For the estimation of noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator (·)HThe conjugate transposition of representing matrix.
3d) calculated by below equation and obtain the first grouped data X1With second packet data X2Cross-covariance R21：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, Q represents pulse number,For the rotation relative to x-axis Invariant factor, operator ()HThe conjugate transposition of representing matrix.
3e) calculated by below equation and obtain the first grouped data X1With the 3rd grouped data X3Cross-covariance R31：
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutFor in the case of having an amplitude phase error Transmitting antenna array, Q represents pulse number,For the rotation relative to y-axis Invariant factor, operator ()HThe conjugate transposition of representing matrix.
3f) by the first grouped data X1Auto-covariance matrix R11s, the first grouped data X1With second packet data X2Cross-covariance R21, the first grouped data X1With the 3rd grouped data X3Cross-covariance R31Sequential combination is number According to covariance matrix.
Step 4, angle on target estimation is carried out using the data covariance matrix, obtains the direction vector of target.
The present embodiment utilizes invariable rotary factor ΛxAnd ΛyThe space angle information of target, the step 4 can be extracted Including following sub-step：
4a) according to below equation pairDo singular value decomposition：
Wherein, R11sFor the first grouped data X1Auto-covariance matrix, R21For the first grouped data X1With second packet number According to X2Cross-covariance,To ask pseudo-inverse operation to accord with, Λx=diag ([λX, 1..., λX, P]) constituted for P characteristic value Diagonal matrix, Uxt=[vXt, 1..., vXt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted.
4b) according to below equation to being set forth in p-th of eigenvalue λX, pComputing is carried out, p-th of target is obtained relative to x-axis Cone angle φX, p：
Wherein, operator ∠ () represents to take multiple angle computing.
4c) according to below equation pairDo singular value decomposition：
Wherein, R31For the first grouped data X1With the 3rd grouped data X3Cross-covariance, R11sFor the first packet count According to X1Auto-covariance matrix,To ask pseudo-inverse operation to accord with, Λy=diag ([λY, 1..., λY, P]) constituted for P characteristic value Diagonal matrix, Uyt=[vYt, 1..., vYt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted.
4d) according to below equation to p-th of eigenvalue λY, pOperation, can obtain p-th of target relative to y-axis Cone angle φY, p：
Wherein, operator ∠ () represents to take multiple angle computing.
The corresponding direction vector r of p-th of target 4e) is calculated according to below equationp：
Wherein φX, pCone angle for p-th of target relative to x-axis, φY, pCone angle for p-th of target relative to y-axis.
Step 5, missed according to the direction vector of target range error respectively to the transmitting antenna array and phase Difference is estimated, obtains the range error estimate and phase error estimation and phase error value of the transmitting antenna array.
It should be noted that having obtained characteristic vector U according to abovementioned stepsxtWith the direction vector r of targetp, Ke Yijie Close the position r of m-th of array element of transmitting antenna arrayT, m=[xm, ym, 0]TEstimate the amplitude phase error of transmitting antenna array.It is described Amplitude phase error includes range error and phase error.
The step 5 includes following sub-step：
The transmitting steering vector a (r of p-th of target when 5a) calculating error free according to below equationp)：
Wherein, rT, 1..., rT, MThe 1st position for launching array element to m-th, operator () are represented respectivelyTRepresent transposition Computing.
5b) according to below equation to p-th of characteristic vector vXt, pNormalization, obtains the transmitting steering vector a (rp) estimate Meter
Wherein, vXt, p(1) v is representedXt, pFirst element value.
The range error estimate ρ of m-th of transmitting array element 5c) is calculated according to below equationm：
Wherein,For transmitting steering vector a (rp) estimationM-th of element, operator | | to ask absolute It is worth symbol.
The phase error estimation and phase error value ψ of m-th of transmitting array element 5d) is calculated according to below equationm：
Wherein,For transmitting steering vector a (rp) estimationM-th of element, aP, mFor transmitting steering vector a (rp) m-th of element, operator ()*Represent conjugate operation.
Due to having been obtained for the range error ρ of all M array elements of transmitting antenna arraym, m=1,2 ..., M, and phase Error ψm, m=1,2 ..., M.Therefore more satisfactory space-time can be obtained by carrying out amplitude phase error compensation to transmission channel Radiation field, and then recover target scene using microwave relevance imaging algorithm.
Step 6, according to the range error estimate and phase error estimation and phase error value of the transmitting antenna array, respectively to described The amplitude and phase of transmitting antenna array are corrected.
By being compensated for transmitting antenna array amplitude and phase, amplitude phase error can be carried out to transmitting antenna array Correction, launches multiple waveforms using the transmitting antenna array after correction, can form accurate space-time random radiation in space , so as to ensure the imaging accuracy of microwave relevance imaging radar.
The effect of the present invention can be further illustrated by following emulation experiment.
One, experimental situations
Reference picture 2, the various parameters used in example of the invention are as shown in table 1：
Parameter name Specific value
Carrier frequency 8GHz
Launching antenna array array structure Uniform surface battle array, array element spacing half-wavelength
Transmitting antenna array array number 9×9
Range error 1dB
Phase error 20 degree
Signal bandwidth 1GHz
Search coverage center and the distance of center of antenna 850m
Parameter name Specific value
Search coverage size 200m×200m
Target is arranged 9 targets are uniformly arranged in search coverage
It is spaced between target X-axis and y-axis direction are spaced 5m
Fast umber of beats 1000
Signal to noise ratio 25dB
The microwave relevance imaging radar parameter of table 1 is set
Two, emulation contents and result
Under described simulated conditions, tested as follows：
Fig. 3 is the range error comparison diagram of the corresponding true amplitude error of 81 array elements and estimation, and Fig. 4 is 81 array elements pair The true phase error and the phase error comparison diagram of estimation answered.It can be seen that from Fig. 3 and Fig. 4 result and utilize the present invention's Microwave relevance imaging radar amplitude and phase error correction method can accurately estimate microwave relevance imaging radar range error and Phase error.
Fig. 5 is the Real profiles of 9 targets of search coverage.When Fig. 6 is without amplitude phase error compensation is carried out, microwave is utilized The imaging results that relevance imaging algorithm is obtained；Fig. 7 is to estimate amplitude phase error using this method and amplitude phase error is compensated Afterwards, the imaging results obtained using microwave relevance imaging algorithm.Comparison diagram 5, Fig. 6 and Fig. 7 can further prove the present invention's Validity, the i.e. present invention effectively On-line Estimation can go out the amplitude phase error of microwave relevance imaging transmitting radar antenna array, and And after amplitude phase error compensation is carried out, the imaging performance of microwave relevance imaging radar is restored.
To sum up, the correctness of this simulating, verifying present invention but linear and reliability.
For foregoing each method embodiment, in order to be briefly described, therefore it is all expressed as to a series of combination of actions, but It is that those skilled in the art should know, the present invention is not limited by described sequence of movement, because according to the present invention, certain A little steps can be carried out sequentially or simultaneously using other.Secondly, those skilled in the art should also know, be retouched in specification The embodiment stated belongs to preferred embodiment, and involved action and the module not necessarily present invention are necessary.
Each embodiment in this specification is described by the way of progressive, what each embodiment was stressed be with Between the difference of other embodiment, each embodiment identical similar part mutually referring to.
The present invention can be described in the general context of computer executable instructions, such as program Module.Usually, program module includes performing particular task or realizes routine, program, object, the group of particular abstract data type Part, data structure etc..The present invention can also be put into practice in a distributed computing environment, in these DCEs, by Remote processing devices connected by communication network perform task.In a distributed computing environment, program module can be with Positioned at including in the local and remote computer-readable storage medium including storage device.
Finally, in addition it is also necessary to explanation, herein, such as first and second or the like relational terms be used merely to by One entity or operation make a distinction with another entity or operation, and not necessarily require or imply these entities or operation Between there is any this actual relation or order.Moreover, term " comprising ", "comprising" or its any other variant meaning Covering including for nonexcludability, so that process, method, commodity or equipment including a series of key elements not only include that A little key elements, but also other key elements including being not expressly set out, or also include be this process, method, commodity or The intrinsic key element of equipment.In the absence of more restrictions, the key element limited by sentence "including a ...", is not arranged Except also there is other identical element in the process including the key element, method, commodity or equipment.
Above to a kind of microwave relevance imaging radar amplitude and phase error correction side based on auxiliary array element provided by the present invention Method, is described in detail, and specific case used herein is set forth to the principle and embodiment of the present invention, the above The explanation of embodiment is only intended to the method and its core concept for helping to understand the present invention；Simultaneously for the general skill of this area Art personnel, according to the thought of the present invention, will change in specific embodiments and applications, in summary, this Description should not be construed as limiting the invention.

Claims (5)

1. a kind of microwave relevance imaging radar amplitude and phase error correction method based on auxiliary array element, it is characterised in that including following Step：
Step 1, the transmitting antenna array of microwave relevance imaging radar launches a variety of transmitted waveforms, the microwave relevance imaging radar Receiving antenna array receive corresponding a variety of echo datas, matched filtering is carried out to the echo data, and to filtered Echo data carry out order arrangement, obtains echo data matrix；Wherein, the receiving antenna array includes three at right angles arranged Individual reception array element；The receiving antenna array and the transmitting antenna array are co-located on same single base radar platform, jointly Constitute a face battle array；
Step 2, the invariable rotary characteristic that array element obtains the echo data matrix is received according to three at right angles arranged, And the first data selection matrix, the second data selection matrix and the 3rd data selection square are constructed according to the invariable rotary characteristic Battle array, and respectively according to the first data selection matrix, the second data selection matrix and the 3rd data selection matrix to described time Element in ripple data matrix is grouped, and obtains corresponding first grouped data, second packet data and the 3rd grouped data；
Step 3, auto-covariance matrix, first grouped data and the second packet number of first grouped data are estimated respectively According to Cross-covariance, first grouped data and the 3rd grouped data Cross-covariance, sequential combination is data Covariance matrix；
Step 4, angle on target estimation is carried out using the data covariance matrix, obtains the direction vector of target；
Wherein, the step 4 includes following sub-step：
4a) according to below equation pairDo singular value decomposition：
Wherein, R11sFor the first grouped data X1Auto-covariance matrix, R21For the first grouped data X1With second packet data X2 Cross-covariance,To ask pseudo-inverse operation to accord with, Λx=diag ([λX, 1..., λX, P]) it is pair that P characteristic value is constituted Angle battle array, Uxt=[vXt, 1..., vXt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted；
4b) according to below equation to being set forth in p-th of eigenvalue λX, pComputing is carried out, cone of p-th of target relative to x-axis is obtained Angle φX, p：
<mrow> <msub> <mi>&amp;phi;</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>arccos</mi> <mo>&amp;lsqb;</mo> <mo>&amp;angle;</mo> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <mi>&amp;lambda;</mi> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
Wherein, operator ∠ () represents to take multiple angle computing；
4c) according to below equation pairDo singular value decomposition：
Wherein, R31For the first grouped data X1With the 3rd grouped data X3Cross-covariance, R11sFor the first grouped data X1 Auto-covariance matrix,To ask pseudo-inverse operation to accord with, Λy=diag ([λY, 1..., λY, P]) for the diagonal of P characteristic value composition Battle array, Uyt=[vYt, 1..., vYt, P] it is the matrix that the corresponding characteristic vector of P characteristic value is constituted；
4d) according to below equation to p-th of eigenvalue λY, pOperation, can obtain cone angle of p-th of target relative to y-axis φY, p：
<mrow> <msub> <mi>&amp;phi;</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>arccos</mi> <mo>&amp;lsqb;</mo> <mo>&amp;angle;</mo> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <mi>&amp;lambda;</mi> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>d</mi> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow>
Wherein, operator ∠ () represents to take multiple angle computing；
The corresponding direction vector r of p-th of target 4e) is calculated according to below equationp：
<mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>cos&amp;phi;</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>cos&amp;phi;</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>,</mo> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;phi;</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>-</mo> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;phi;</mi> <mrow> <mi>y</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> </mrow> </msqrt> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
Wherein φX, pCone angle for p-th of target relative to x-axis, φY, pCone angle for p-th of target relative to y-axis；
Step 5, the range error and phase error of the transmitting antenna array are entered respectively according to the direction vector of the target Row estimation, obtains the range error estimate and phase error estimation and phase error value of the transmitting antenna array；
Step 6, according to the range error estimate and phase error estimation and phase error value of the transmitting antenna array, respectively to the transmitting The amplitude and phase of aerial array are corrected.
2. the microwave relevance imaging radar amplitude and phase error correction method according to claim 1 based on auxiliary array element, it is special Levy and be, the step 1 includes following sub-step：
1a) transmitting antenna array of microwave relevance imaging radar includes M transmitting array element, and the M transmitting array element transmitting is a variety of Transmitted waveform, the complex envelope of the transmitted waveform of m-th of transmitting array element is sm, wherein M is natural number, and m is natural number, and m= 1 ..., M；
1b) receiving antenna array of microwave relevance imaging radar includes N number of reception array element, and N number of reception array element receives correspondence A variety of echo datas, it is y to receive the echo data of q subpulses that array element receives for n-thN, q, wherein N is natural number, n For natural number, and n=1 ..., N, N=3；
1c) by N number of echo data for receiving the q subpulses that array element is received and the transmitted wave of described M transmitting array element The conjugation of the complex envelope of shape makees inner product, obtains corresponding matched filtering output xq, wherein xq(n-1) M+m element be Represent the echo data y of q subpulses for receiving described n-th reception array elementN, qWith m-th of transmitting array element Transmitted waveform complex envelope smConjugation make after inner product, obtain corresponding matched filtering output,Pass through below equation meter Obtain：
Wherein, n=1 ..., N；M=1 ..., M；Q=1 ..., Q, Q represent pulse number, and M, m, N, n, Q, q are natural number；
N number of reception array element corresponding matched filtering output 1d) is lined up into a row according to subscript m and subscript n order successively Vector, obtains the matched filtering result x of q subpulsesq；
Matched filtering output result of the array element for the complex envelope of the transmitted waveform of M transmitting array element is received under by n-th Mark m orders line up a column vector
WillA column vector x is lined up according to subscript n orderq：
Wherein, operator ()TTransposition computing is represented, oeprator * represents that Khatri-Rao is accumulated, nqFor additive white Gaussian noise, bqTo obey the target complex scattering coefficients of Swerling II types, ArFor receiving antenna array steering vector, AutTo there is amplitude phase error In the case of transmitting antenna array steering vector；
Le) the matched filtering result x for respectively obtaining Q pulseqA matrix is lined up according to subscript q orders, Q are obtained The echo data matrix X of pulse：
X=[x1..., xQ]=(Ar*Aut)B+W
Wherein, B represents the target scattering coefficient matrix of Q subpulses, B=[b1..., bQ]；W represents the additivity white noise of Q subpulses Sound matrix, W=[n1..., nQ]。
3. the microwave relevance imaging radar amplitude and phase error correction method according to claim 1 based on auxiliary array element, it is special Levy and be, the step 2 includes following sub-step：
2a) array elements are received according to described at right angles arrange three obtain rotation in the echo data matrix between element not Become characteristic, and the first data selection matrix, the second data selection matrix and the 3rd are constructed respectively according to the invariable rotary characteristic Data selection matrix, wherein the first data selection matrix is：
<mrow> <msub> <mi>J</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>&amp;rsqb;</mo> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>M</mi> </msub> </mrow>
Second data selection matrix is：
<mrow> <msub> <mi>J</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&amp;rsqb;</mo> <mo>&amp;CircleTimes;</mo> <msub> <mi>I</mi> <mi>M</mi> </msub> </mrow>
3rd data selection matrix is：
Wherein, IMThe unit matrix tieed up for M × M,Represent Kronecker products；
2b) using the first data selection matrix, the second data selection matrix and the 3rd data selection matrix respectively to described Element in echo data matrix X is selected and is grouped, and obtains corresponding first grouped data, comprising the invariable rotary factor Second packet data and the 3rd grouped data comprising the invariable rotary factor, wherein the first grouped data is：
X1=J1X=AutB+J1W
Second packet data are：X2=J2X=AutΛxB+J2W
3rd grouped data is：
X3=J3X=AutΛyB+J3W
Wherein,For the invariable rotary factor relative to x-axis,For the invariable rotary factor relative to y-axis.
4. the microwave relevance imaging radar amplitude and phase error correction method according to claim 1 based on auxiliary array element, it is special Levy and be, the step 3 includes following sub-step：
3a) calculated by below equation and obtain the first grouped data X1Autocorrelation matrix R11：
<mrow> <msub> <mi>R</mi> <mn>11</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>X</mi> <mn>1</mn> </msub> <msup> <msub> <mi>X</mi> <mn>1</mn> </msub> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>R</mi> <mi>B</mi> </msub> <msup> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mi>H</mi> </msup> <mo>+</mo> <msup> <msub> <mi>&amp;sigma;</mi> <mi>n</mi> </msub> <mn>2</mn> </msup> <msub> <mi>I</mi> <mi>M</mi> </msub> </mrow>
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutTo there is the hair in the case of amplitude phase error Penetrate aerial array, σn 2For noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator ()HRepresent square The conjugate transposition of battle array；
3b) by below equation to the first grouped data X1Autocorrelation matrix R11Eigenvalues Decomposition is carried out, noise power is obtained Estimation
<mrow> <msub> <mi>R</mi> <mn>11</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>r</mi> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>r</mi> </msub> <msubsup> <mi>U</mi> <mi>r</mi> <mi>H</mi> </msubsup> </mrow>
<mrow> <msup> <msub> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>M</mi> <mo>-</mo> <mi>Q</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mrow> <mi>r</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow>
Wherein, the diagonal matrix Λ that characteristic vector is constitutedr=diag ([λR, 1, λR, 2..., λR, M]), wherein λR, 1≥λR, 2≥... ≥λR, M, UrIt is characterized the matrix of vector composition, operator ()HThe conjugate transposition of representing matrix, Q represents pulse number, and M is represented The element number of array of transmitting antenna array；
3c) by the estimation of noise powerFrom the first grouped data X1Autocorrelation matrix R11It is middle to deduct, obtain the first packet count According to X1Auto-covariance matrix R11s：
<mrow> <msub> <mi>R</mi> <mrow> <mn>11</mn> <mi>s</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>R</mi> <mn>11</mn> </msub> <mo>-</mo> <msup> <msub> <mover> <mi>&amp;sigma;</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mn>2</mn> </msup> <msub> <mi>I</mi> <mi>M</mi> </msub> <mo>&amp;ap;</mo> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>R</mi> <mi>B</mi> </msub> <msup> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mi>H</mi> </msup> </mrow>
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutTo there is the transmitting in the case of amplitude phase error Aerial array,For the estimation of noise power, Q represents pulse number, IMRepresent M × M unit matrix, operator ()HTable Show the conjugate transposition of matrix；
3d) calculated by below equation and obtain the first grouped data X1With second packet data X2Cross-covariance R21：
<mrow> <msub> <mi>R</mi> <mn>21</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>X</mi> <mn>2</mn> </msub> <msup> <msub> <mi>X</mi> <mn>1</mn> </msub> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>x</mi> </msub> <msub> <mi>R</mi> <mi>B</mi> </msub> <msup> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mi>H</mi> </msup> </mrow>
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutTo there is the transmitting in the case of amplitude phase error Aerial array, Q represents pulse number,For the invariable rotary relative to x-axis because Son, operator ()HThe conjugate transposition of representing matrix；
3e) calculated by below equation and obtain the first grouped data X1With the 3rd grouped data X3Cross-covariance R31：
<mrow> <msub> <mi>R</mi> <mn>31</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <msub> <mi>X</mi> <mn>3</mn> </msub> <msup> <msub> <mi>X</mi> <mn>1</mn> </msub> <mi>H</mi> </msup> <mo>=</mo> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <msub> <mi>&amp;Lambda;</mi> <mi>y</mi> </msub> <msub> <mi>R</mi> <mi>B</mi> </msub> <msup> <msub> <mi>A</mi> <mrow> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mi>H</mi> </msup> </mrow>
Wherein,B represents the target scattering coefficient matrix of Q subpulses, AutTo there is the transmitting in the case of amplitude phase error Aerial array, Q represents pulse number,For the invariable rotary relative to y-axis because Son, operator ()HThe conjugate transposition of representing matrix；
3f) by the first grouped data X1Auto-covariance matrix R11s, the first grouped data X1With second packet data X2's Cross-covariance R21, the first grouped data X1With the 3rd grouped data X3Cross-covariance R31Sequential combination is assisted for data Variance matrix.
5. the microwave relevance imaging radar amplitude and phase error correction method according to claim 1 based on auxiliary array element, it is special Levy and be, the step 5 includes following sub-step：
The transmitting steering vector a (r of p-th of target when 5a) calculating error free according to below equationp)：
<mrow> <mi>a</mi> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <msup> <msub> <mi>r</mi> <mrow> <mi>t</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>r</mi> <mi>p</mi> </msub> </mrow> </msup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <msup> <msub> <mi>r</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>M</mi> </mrow> </msub> <mi>T</mi> </msup> <msub> <mi>r</mi> <mi>p</mi> </msub> </mrow> </msup> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
Wherein, rT, 1..., rT, MThe 1st position for launching array element to m-th, operator () are represented respectivelyTRepresent transposition computing；
5b) according to below equation to p-th of characteristic vector vXt, pNormalization, obtains the transmitting steering vector a (rp) estimation
<mrow> <mover> <mi>a</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mi>t</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>v</mi> <mrow> <mi>x</mi> <mi>t</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>P</mi> </mrow>
Wherein, vXt, p(1) v is representedXt, pFirst element value；
The range error estimate ρ of m-th of transmitting array element 5c) is calculated according to below equationm：
<mrow> <msub> <mi>&amp;rho;</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>P</mi> </munderover> <mo>|</mo> <msub> <mover> <mi>a</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mo>|</mo> </mrow> <mi>P</mi> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> </mrow>
Wherein,For transmitting steering vector a (rp) estimationM-th of element, operator | | to ask absolute value to accord with Number；
The phase error estimation and phase error value ψ of m-th of transmitting array element 5d) is calculated according to below equationm：
<mrow> <msub> <mi>&amp;psi;</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>P</mi> </munderover> <mo>&amp;angle;</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>a</mi> <mo>^</mo> </mover> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <msubsup> <mi>a</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>m</mi> </mrow> <mo>*</mo> </msubsup> <mo>)</mo> </mrow> </mrow> <mi>P</mi> </mfrac> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>M</mi> </mrow>
Wherein,For transmitting steering vector a (rp) estimationM-th of element, aP, mFor transmitting steering vector a's (rp) M-th of element, operator ()*Represent conjugate operation.
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