CN110376560A - A kind of airborne bistatic MIMO radar amplitude and phase error correction method based on single range gate - Google Patents
A kind of airborne bistatic MIMO radar amplitude and phase error correction method based on single range gate Download PDFInfo
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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
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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
- G01S7/4004—Means for monitoring or calibrating of parts of a radar system
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Abstract
The invention discloses a kind of airborne bistatic MIMO radar amplitude and phase error correction method based on single range gate, include: that there are the data of array element amplitude phase error in receiver one range gate of reception, processing is corrected to echo data by an error correction matrix to be asked；Pitch angle and azimuth of all clutter scattering points relative to transmitter and receiver in single range gate are calculated according to airborne bistatic MIMO radar model, three-dimensional steering vector when calculating the sky of all clutter scattering points using angle information is orthogonalized the projection matrix that clutter Orthogonal Subspaces complementary space is calculated after processing to steering vector；Projection matrix is multiplied with the data after correction using the property of projection matrix, seeks minimum two norms, and uses first array element of Virtual array as reference array element structure constraint condition, acquires error correction matrix using constraint condition calculating.It is compared with the traditional method, method computational accuracy of the invention is higher, increases the stability under non-homogeneous clutter environment.
Description
Technical field
The invention belongs to radar transmit-receive array amplitude and phase error correction technical field, and in particular to a kind of based on single range gate
Airborne bistatic MIMO radar amplitude and phase error correction method.
Background technique
Multiple-input and multiple-output (Multiple-Input Multiple-Output, MIMO) radar in transmitting terminal and connects respectively
Receiving end configures multiple array elements, and all transmitting array element emits mutually orthogonal signal simultaneously, receives array element using transmitting signal
Orthogonality is distinguished signal is emitted, and material is thus formed virtual arrays, improve the accuracy of parameter Estimation.It is airborne biradical
The operating mode that ground radar transmitter and receiver are split has many advantages, such as targetedly to Stealthy Target, low
Air transportion moving-target, jamming target are detected, and receiver can afield move hidden investigation according to demand, increase detection
Range, transmitter are passive radar, substantially increase survival ability.Airborne bistatic MIMO radar is by biradical system and MIMO body
System is joined together, and mutual supplement with each other's advantages is realized, and has not only had advantage of bistatic radar in terms of anti-stealthy, hidden, but also real
The increase for having showed freedom degree, under airborne bistatic MIMO system, by the way that target can be obtained simultaneously to the processing for receiving data
Relative to the angle information of transmitter and receiver, efficiently using to launch angle information can be how general by reception space-
Strangling two-dimentional clutter spectrum becomes emission space-reception space-Doppler's three-dimensional clutter spectrum.
Radar under airborne bistatic MIMO system is in lower view operating mode, so that the backward energy of land clutter is much big
In target energy, how to realize that effective inhibition to land clutter is the key that target detection.When transmitting array element is deposited with array element is received
In amplitude phase error, the clutter recognition performance and target detection performance of radar are by sharp fall.General traditional active correction
Method needs the position of known calibration source, and airborne radar is kept in motion, so that the position of calibration source can not determine, thus
It cannot achieve the correction to amplitude phase error；Amplitude phase error Self-Tuning Algorithm can simultaneously error and target angle are estimated,
But need to carry out successive ignition and acquire optimal solution, the number of iterations is easy by selected initial value affecting, and in iterative process
Locally optimal solution is fallen into, therefore airborne bistatic MIMO radar is not available traditional amplitude phase error automatic correcting method.
In order to realize the correction to airborne bistatic MIMO radar amplitude phase error, Zheng Yu et al. proposes empty based on clutter
Between characteristic airborne MIMO radar amplitude phase error Self-Tuning Algorithm, the algorithm using clutter subspace and noise subspace mutually just
The characteristic of friendship acquires amplitude and phase error correction matrix, realizes the correction to amplitude phase error.But the correction square that the algorithm finally obtains
Battle array is needed using clutter plus noise covariance matrix and projection matrix, and the accuracy meeting that covariance matrix and projection matrix calculate
Influence final correction as a result, clutter plus noise covariance matrix is estimated by training sample, and training samples number
Size and correction of a final proof effect it is closely related, when number of training is less, correction accuracy reduce；To the meter of projection matrix
Calculation is also needed using echo data, therefore the accuracy of the calculating of projection matrix is also influenced by echo data.
Summary of the invention
In order to solve the above-mentioned problems in the prior art, it is airborne double based on single range gate that the present invention provides a kind of
Base MIMO radar amplitude and phase error correction method.The technical problem to be solved in the present invention is achieved through the following technical solutions:
A kind of airborne bistatic MIMO radar amplitude and phase error correction method based on single range gate, it is described airborne bistatic
The transmitter of MIMO radar is the even linear array for including M array element, and receiver is the even linear array for including N number of array element, detects model
It encloses and is divided into L range gate, wherein M, N and L are positive integer, and described method includes following steps:
Step 1, an airborne bistatic MIMO radar range gate l to be detected in detectable range is obtained to return
Wave number is according to xl, l is 1 to an integer value between L, the echo data xlIn only include clutter information and noise information, and
The echo data xlThere are the amplitude phase errors of array element；
Step 2, the range gate l is divided into NcA clutter scattering point, calculates the NcA clutter scattering point is relative to hair
Penetrate the azimuth angle theta of machinetAnd pitch angleThe NcAzimuth angle theta of a clutter scattering point relative to receiverrAnd pitch angle
According to the azimuth angle theta being calculatedt, the pitch angleThe azimuth angle thetarWith the pitch angleCalculate each institute
State the normalization Doppler frequency f of clutter scattering pointd,i, normalized emission spatial frequency ft,iWith normalization reception space frequency
fr,i, then according to the normalization Doppler frequency fd,i, the normalized emission spatial frequency ft,iIt is received with the normalization
Spatial frequency fr,iThree-dimensional is oriented to column vector when calculating the sky of each clutter scattering point, later by the NcA clutter dissipates
Three-dimensional guide row vectorial structure is at a matrix when sky of exit point；
Step 3, N step 2 obtained using Schmidt orthogonalization methodcThe empty Shi Sanwei of a clutter scattering point
Guide row vectorial structure at matrix be orthogonalized processing, obtain one group of orthogonal basis, the orthogonal basis utilized to calculate clutter
The projection matrix of orthogonal space complementary space
Step 4, amplitude and phase error correction matrix T is set, using the amplitude and phase error correction matrix T to there are amplitude phase errors
Receive data xlIt is corrected processing, by the reception data x after correctionlWith the projection square of the clutter Orthogonal Subspaces complementary space
Battle arrayIt is multiplied, using first array element of Virtual array as reference array element structure constraint condition, calculates the amplitude and phase error correction
Matrix T；
Step 5, it is missed using range error and phase of the amplitude and phase error correction matrix T to airborne bistatic MIMO radar
Difference is corrected.
In one embodiment of the invention, the echo data x of the step 1lExpression formula are as follows:
In formula, xcIndicate clutter data, N indicates noise data and sets noise as white Gaussian noise, ρiWhat expression received
The echo size of i-th of clutter scattering point, a (ft,i) indicate i-th of clutter scattering point normalized emission steering vector, b
(fr,i) indicate that the normalization of i-th of clutter scattering point receives steering vector, c (fd,i) indicate i-th of clutter scattering point normalizing
Change Doppler's steering vector, s (ft,i,fr,i,fd,i) indicate three-dimensional steering vector when the sky of i-th of clutter scattering point.
In one embodiment of the invention, the step 2 specifically comprises the following steps:
(2a) is according to the transmitter, the receiver and the NcAny one clutter scattering in a clutter scattering point
The coordinate information of point P calculates separately the spacing R of the clutter scattering point P and transmittertWith the spacing R of receiverr, the clutter
The spacing R of scattering point P and the transmittertWith the spacing R of the clutter scattering point P and the receiverrExpression formula difference
Are as follows:
In formula, the coordinate of the transmitter is denoted as (xt,yt,zt), the coordinate of the receiver is denoted as (xr,yr,zr), it will
The coordinate of the clutter scattering point P is denoted as (xP,yP,0)；
According to the transmitter, the receiver and the NcAny one clutter scattering point P in a clutter scattering point
Coordinate information and the spacing RtWith spacing RrCalculate the azimuth angle theta of the clutter scattering point P and the transmittertWith bow
The elevation angleThe azimuth angle theta of the clutter scattering point P and the receiverrAnd pitch angleThe azimuth angle thetat, the pitching
AngleThe azimuth angle thetarWith the pitch angleExpression formula be respectively as follows:
(2b) is according to the azimuth angle thetat, the pitch angleThe azimuth angle thetarWith the pitch angleDescribed in calculating
The normalization Doppler frequency f of clutter scattering point Pd,i, normalized emission spatial frequency ft,iAnd normalization reception space frequency
fr,i, the normalization Doppler frequency fd,i, the normalized emission spatial frequency ft,iWith the normalization reception space frequency
fr,iExpression formula be respectively as follows:
(2c) is according to the normalized emission spatial frequency ft,iObtain emission space steering vector a (ft,i), according to described
Normalize reception space frequency fr,iObtain reception space steering vector b (fr,i), according to the normalization Doppler frequency fd,i?
To Doppler steering vector c (fd,i), the emission space steering vector a (ft,i), the reception space steering vector b (fr,i)
With Doppler's steering vector c (fd,i) expression formula be respectively as follows:
(2d) calculates the emission space steering vector a of each clutter scattering point according to step (2a)~(2c)
(ft,i), the reception space steering vector b (fr,i) and Doppler's steering vector c (fd,i), and according to miscellaneous described in each
The emission space steering vector a (f of wave dispersion exit pointt,i), the reception space steering vector b (fr,i) and the Doppler lead
To vector C (fd,i) three-dimensional steering vector when the sky of each clutter scattering point is obtained, three-dimensional steering vector when described empty
Expression formula are as follows:
In formula, s (ft,i,fr,i,fd,i) indicate three-dimensional steering vector when the sky of i-th of clutter scattering point；
Later by the NcThree-dimensional guide row vectorial structure is at a matrix when sky of a clutter scattering point.
In one embodiment of the invention, the step 4 specifically comprises the following steps:
Emission array amplitude phase error is defined as e by (4a)t, the expression formula of emission array amplitude phase error are as follows:
et=[ρt,1,ρt,2..., ρt,M]T
In formula, ρt,iI=1,2 ..., M indicate amplitude phase error existing for i-th of transmitting array element,Wherein,
γt,iIndicate range error existing for i-th of transmitting array element, ξt,iIndicate phase error existing for i-th of transmitting array element；
Receiving array amplitude phase error is defined as er, it is expressed by following formula:
er=[ρr,1,ρr,2..., ρr,N]T
In formula, ρr,iI=1,2 ..., N indicate amplitude phase error existing for i-th of reception array element,Wherein,
γr,iIndicate range error existing for i-th of reception array element, ξr,iIndicate phase error existing for i-th of reception array element；
At this point, emission space guiding becomesWherein Γet=diag (et) indicate emission array
Amplitude phase error etDiagonal matrix is pulled into, reception space steering vector becomesWherein, Γer=diag (er)
It indicates the amplitude phase error e of receiving arrayrPull into diagonal matrix；
Three-dimensional steering vector becomes when receiving the sky of data:
(4a) sets the amplitude and phase error correction matrix T of the airborne bistatic MIMO radar array element, the amplitude phase error school
Positive matrices T meets relational expression Τ=Γ-1, according to the relational expression to Γ, the expression formula of the amplitude and phase error correction matrix T are as follows:
In formula, column vector taIn element and the emission array amplitude phase error etElement and the receiving array
Amplitude phase error erElement correspond, the column vector taEach of element be the emission array amplitude phase error et
With the amplitude phase error e of the receiving arrayrIn each corresponding element inverse, the column vector taExpression formula are as follows:
In formula, 1MN×1It indicates the column vector that MN × 1 is tieed up and whole elements is that 1, Θ is indicated the width phase of the emission array
Error etWith the amplitude phase error e of the receiving arrayrIn each corresponding element be divided by；
The amplitude and phase error correction matrix T is multiplied with the data x (l) there are error, is obtained:
Τ x (l)=Τ Γ xc(l)+Τ N=xc(l)+ΤN
In formula, xc(l) clutter data is indicated, N indicates noise data；
Set space CnBy L and M, the two subspaces are constituted, in space CnIn have any x ∈ Cn, and Unique Decomposition of Ring are as follows:
X=y+z y ∈ L, z ∈ M
In formula, y indicates x along the projection of M to L；
Set projection operator PL,M, the projection operator PL,MExpression formula be shown below:
PL,MX=y
In formula, projection operator PL,MIndicate by any x along M to L progress projective transformation, if x in the L of subspace, then
PL,MX=x, if x in the M of subspace, then PL,MX=0；
Set the projection matrix of the clutter Orthogonal Subspaces complementary spaceThe then projection matrixWith clutter data
xc(l) being multiplied is 0, i.e.,Then by the projection matrixThe amplitude and phase error correction matrix T and institute
It states there are the data x (l) of error multiplication, obtains following expression:
The amplitude and phase error correction matrix T, the expression formula of the constraint formula are calculated by structure constraint formula later are as follows:
In formula, h=[1,0,0 ..., 0]1×MN, hta=1 indicates first array element of Virtual array to be reference array element, by
In the projection matrixFor orthogonal intersection cast shadow matrix, therefore the projection matrixNot only meet Hermite condition, also meets
Idempotent condition, soThen the constraint formula variation is the first constraint formula, the expression of the first constraint formula
Formula are as follows:
Later, first by x (l) diagonalization to become diagonal matrix, then X=diag (x (l)), then mutually misses the width
Element extraction in poor correction matrix T on diagonal line comes out, and being put into a dimension is to be by the dimension in the column vector of NK × 1
The column vector of NK × 1 is denoted as t, then Τ x (l)=Xt, then the first constraint formula variation is the second constraint formula, second constraint
The expression formula of formula are as follows:
In formula, t and taRelationship beIt willIt is denoted as B, then second constraint
Formula variation is that third constrains formula, the expression formula of the third constraint formula are as follows:
And it willIt is denoted as A, then the third constraint formula variation is the 4th constraint formula, the 4th constraint formula
Expression formula are as follows:
The 4th constraint formula is solved using method of Lagrange multipliers, obtains column vector taAre as follows:
According to the column vector taWith the relationship of the amplitude and phase error correction matrix T, the amplitude and phase error correction square is obtained
Battle array T.
Beneficial effects of the present invention:
The present invention utilizes the projection of the geometry calculation clutter Orthogonal Subspaces complementary space of airborne bistatic MIMO radar
Matrix, the echo data for not using receiver to receive avoid estimation to covariance matrix and to covariance matrix
Feature decomposition, reduce the demand to training sample, improve the amplitude and phase error correction process under non-homogeneous clutter environment
Accuracy, and the reasoning flow of amplitude and phase error correction matrix is optimized, improve calculating speed.
The present invention is described in further details below with reference to accompanying drawings and embodiments.
Detailed description of the invention
Fig. 1 is a kind of airborne bistatic MIMO radar amplitude phase error school based on single range gate provided in an embodiment of the present invention
The flow diagram of correction method；
Fig. 2 is another airborne bistatic MIMO radar amplitude phase error based on single range gate provided in an embodiment of the present invention
The flow diagram of bearing calibration；
Fig. 3 is the geometric configuration schematic diagram of the airborne bistatic MIMO radar of one kind provided in an embodiment of the present invention；
Fig. 4 is a kind of use the method for the present invention and IAD-SR-STAP method provided in an embodiment of the present invention respectively to amplitude
The comparison diagram of correction；
Fig. 5 is a kind of use the method for the present invention and IAD-SR-STAP method provided in an embodiment of the present invention respectively to phase
The comparison diagram of correction；
Fig. 6 is that there are be corrected when range error to array element for a kind of use the method for the present invention provided in an embodiment of the present invention
Improvement factor comparison diagram；
Fig. 7 is that there are be corrected when phase error to array element for a kind of use the method for the present invention provided in an embodiment of the present invention
Improvement factor comparison diagram.
Bearing calibration of the invention realizes the correction to amplitude phase error by the data of single range gate, in correction course
The clutter Orthogonal Subspaces complementary space projection matrix used is obtained by the geometry calculation of airborne bistatic MIMO radar,
Influence of the echo data to projection matrix is avoided, calculating speed is greatly improved with counting accuracy；What the algorithm finally acquired
The data that single range gate has been only used in correction matrix, avoiding the non-homogeneous bring of sample influences, and increases amplitude phase error
The stability of correction improves the accuracy of amplitude and phase error correction.
Specific embodiment
Further detailed description is done to the present invention combined with specific embodiments below, but embodiments of the present invention are not limited to
This.
Embodiment one
Referring to Figure 1 and Fig. 2, Fig. 1 are provided in an embodiment of the present invention a kind of based on the airborne bistatic of single range gate
The flow diagram of MIMO radar amplitude and phase error correction method, Fig. 2 are provided in an embodiment of the present invention another based on single distance
The flow diagram of the airborne bistatic MIMO radar amplitude and phase error correction method of door.The present embodiment provides one kind based on single distance
The airborne bistatic MIMO radar amplitude and phase error correction method of door, the transmitter of the airborne bistatic MIMO radar be include M
The even linear array of array element, receiver are the even linear array for including N number of array element, and even linear array is uniform line-array, and transmitter
The signal of M array element transmitting be mutually orthogonal waveform signal, the umber of pulse received in a Coherent processing time interval
For K, and detection range is divided into L range gate, wherein M, N, K and L are positive integer, should be based on the airborne bistatic of single range gate
MIMO radar amplitude and phase error correction method includes step 1 to step 5, in which:
Step 1, the number of echoes of an airborne bistatic MIMO radar range gate l to be detected in detectable range is obtained
According to xl, l is 1 to an integer value between L, echo data xlIn only include clutter information and noise information, and number of echoes
According to xlThere are the amplitude phase errors of array element；
Specifically, the echo data x for some range gate l that receiver receiveslIt can indicate are as follows:
In formula, xcIndicate clutter data, N indicates noise data and sets noise as white Gaussian noise, ρiWhat expression received
The echo size of i-th of clutter scattering point, ρiEqually with the reflection coefficient of the transmit-receive position figure of radar and clutter scattering point surface
It is related, if it is in ideal conditions, ρiGaussian distributed, a (ft,i) indicate that the normalization of i-th of clutter scattering point is sent out
Penetrate steering vector, b (fr,i) indicate that the normalization of i-th of clutter scattering point receives steering vector, c (fd,i) indicate i-th of clutter
Normalization Doppler's steering vector of scattering point, s (ft,i,fr,i,fd,i) indicate that three-dimensional is oriented to when the sky of i-th of clutter scattering point
Vector.
Step 2, three-dimensional steering vector when calculating the sky of each clutter scattering point；
Specifically, range gate l is divided into NcA clutter scattering point calculates NcA clutter scattering point is relative to transmitter
Azimuth angle thetatAnd pitch angleNcAzimuth angle theta of a clutter scattering point relative to receiverrAnd pitch angleAccording to calculating
The azimuth angle theta arrivedt, pitch angleAzimuth angle thetarAnd pitch angleCalculate the normalization Doppler frequency of each clutter scattering point
fd,i, normalized emission spatial frequency ft,iWith normalization reception space frequency fr,i, then according to normalization Doppler frequency fd,i、
Normalized emission spatial frequency ft,iWith normalization reception space frequency fr,iThree-dimensional is led when calculating the sky of each clutter scattering point
To column vector, later by NcThree-dimensional guide row vectorial structure is at a matrix when sky of a clutter scattering point；
Further, step 2 may include step (2a) to (2d), in which:
(2a) refers to Fig. 3, and the coordinate of transmitter is denoted as (xt,yt,zt), the coordinate of receiver is denoted as (xr,yr,zr),
The range gate l chosen in step 1 is evenly dividing as NcA clutter scattering point, by NcAny one in a clutter scattering point is miscellaneous
The coordinate of wave dispersion exit point P is denoted as (xP,yP, 0), distinguished later according to the coordinate information of transmitter, receiver and clutter scattering point P
Calculate the spacing R of the clutter scattering point P and transmittertWith the spacing R of receiverr, between clutter scattering point P and the transmitter
Away from RtWith the spacing R of the clutter scattering point P and the receiverrExpression formula be respectively as follows:
Later according to the coordinate information and spacing R of transmitter, receiver and clutter scattering point PtWith spacing RrCalculate clutter
The azimuth angle theta of scattering point P and transmittertAnd pitch angleThe azimuth angle theta of clutter scattering point P and receiverrAnd pitch angle
The azimuth angle theta of clutter scattering point P and transmittert, clutter scattering point P and transmitter azimuth pitch angleClutter scattering point P
With receiver orientations angle θr, clutter scattering point P and receiver pitch angleExpression formula be respectively as follows:
(2b) is according to azimuth angle thetat, pitch angleAzimuth angle thetarAnd pitch angleThe normalization for calculating clutter scattering point P is more
General Le frequency fd,i, normalized emission spatial frequency ft,iAnd normalization reception space frequency fr,i, normalize Doppler frequency
fd,i, normalized emission spatial frequency ft,iWith normalization reception space frequency fr,iExpression formula be respectively as follows:
(2c) is according to the obtained normalized emission spatial frequency f of step (2b)t,iObtain emission space steering vector a
(ft,i), according to normalization reception space frequency fr,iObtain reception space steering vector b (fr,i), according to normalization Doppler's frequency
Rate fd,iObtain Doppler steering vector c (fd,i), emission space steering vector a (ft,i), reception space steering vector b (fr,i) and
Doppler steering vector c (fd,i) expression formula be respectively as follows:
(2d) calculates the emission space steering vector a (f of each clutter scattering point according to step (2a)~(2c)t,i), connect
Receive steric direction vector b (fr,i) and Doppler steering vector c (fd,i), and led according to the emission space of each clutter scattering point
To vector a (ft,i), reception space steering vector b (fr,i) and Doppler steering vector c (fd,i) obtain each clutter scattering point
Sky when three-dimensional steering vector, the expression formula of three-dimensional steering vector when empty are as follows:
In formula, s (ft,i,fr,i,fd,i) indicate three-dimensional steering vector when the sky of i-th of clutter scattering point；
Later by NcThree-dimensional guide row vectorial structure is at a matrix when sky of a clutter scattering point.
Step 3, three-dimensional steering vector matrix is calculating clutter subspace just when the sky of the clutter scattering point obtained using step 2
Hand over the projection matrix of complementary space
Specifically, N step 2 obtained using Schmidt orthogonalization methodcThree-dimensional is oriented to when the sky of a clutter scattering point
Column vector is constructed of matrix and is orthogonalized processing, obtains one group of orthogonal basis, calculates clutter Orthogonal Subspaces using orthogonal basis
The projection matrix of complementary space
Furthermore, it is understood that defining clutter subspace Vc, will be all miscellaneous in range gate l using Schmidt orthogonalization method
Scattering of wave point is orthogonalized standardization processing, obtains one group of orthogonal basis, constructs clutter subspace, clutter using this group of orthogonal basis
Subspace VcExpression formula are as follows:
By clutter subspace VcThis group of orthogonal basis can be in the hope of its projection matrix Pc, and projection matrixThat
Clutter subspace VcThe orthogonal complement space projection matrixExpression formula are as follows:
In formula, I is unit matrix.
Step 4, amplitude and phase error correction matrix T is calculated.
Specifically, amplitude and phase error correction matrix T is set, using amplitude and phase error correction matrix T to there are amplitude phase errors to connect
Receive data xlIt is corrected processing, by the reception data x after correctionlWith the projection matrix of clutter Orthogonal Subspaces complementary spacePhase
Multiply, using first array element of Virtual array as reference array element structure constraint condition, calculates amplitude and phase error correction matrix T.
Further, step 4 may include step (4a) to (4b), in which:
(4a) carries out mathematical expression to airborne bistatic MIMO radar amplitude phase error model, i.e., by emission array amplitude phase error
It is defined as et, emission array amplitude phase error etExpression formula are as follows:
et=[ρt,1,ρt,2..., ρt,M]TFormula 17
In formula, ρt,iAmplitude phase error existing for i-th of transmitting array element of expression, i=1,2 ..., M, andIts
In, γt,iIndicate range error existing for i-th of transmitting array element, ξt,iIndicate phase error existing for i-th of transmitting array element.
Receiving array amplitude phase error is defined as er, it is expressed by following formula:
er=[ρr,1,ρr,2..., ρr,N]TFormula 18
In formula, ρr,iAmplitude phase error existing for i-th of reception array element of expression, r=1,2 ..., N, andIts
In, γ r,iIndicate range error existing for i-th of reception array element, ξr,iIndicate phase error existing for i-th of reception array element.
At this point, emission space guiding becomesWherein Γet=diag (et) indicate emission array
Amplitude phase error etDiagonal matrix is pulled into, reception space steering vector becomesWherein, Γer=diag (er)
It indicates the amplitude phase error e of receiving arrayrPull into diagonal matrix.
Three-dimensional steering vector becomes when receiving the sky of data:
(4b) calculates airborne bistatic MIMO radar array element amplitude and phase error correction matrix T；
The amplitude and phase error correction matrix T of airborne bistatic MIMO radar array element is set, amplitude and phase error correction matrix T, which meets, to close
It is formula Τ=Γ-1, according to the relational expression to Γ, the expression formula of the amplitude and phase error correction matrix T are as follows:
In formula, column vector taIn element and emission array amplitude phase error etElement and receiving array amplitude phase error
erElement correspond, column vector taEach of element be emission array amplitude phase error etWith the width phase of receiving array
Error erIn each corresponding element inverse, column vector taExpression formula are as follows:
In formula, 1MN×1It indicates the column vector that MN × 1 is tieed up and whole elements is that 1, Θ is indicated the width phase of the emission array
Error etWith the amplitude phase error e of the receiving arrayrIn each corresponding element be divided by；
Amplitude and phase error correction matrix T is multiplied with the data x (l) there are error, can be obtained:
Τ x (l)=Τ Γ xc(l)+Τ N=xc(l)+Τ N formula 22
In formula, xc(l) clutter data is indicated, N indicates noise data, and the data after correcting are divided into two parts, first
It is divided into the clutter data there is no error, second part is the noise data being multiplied with correction data.
Set space CnBy L and M, the two subspaces are constituted, in space CnIn have any x ∈ Cn, and can uniquely divide
Solution are as follows:
X=y+z y ∈ L, z ∈ M formula 23
In formula, y indicates x along the projection of M to L；
Set projection operator PL,M, the projection operator PL,MExpression formula be shown below:
PL,MX=y formula 24
In formula, projection operator PL,MIndicate by any x along M to L progress projective transformation, if x in the L of subspace, then
PL,MX=x, if x in the M of subspace, then PL,MX=0；
Set the projection matrix of clutter Orthogonal Subspaces complementary spaceAccording to property above, then projection matrixWith
Clutter data xc(l) being multiplied is 0, i.e.,Then by projection matrixIt is multiplied to obtain such as following table with formula 22
Up to formula:
The clutter data in echo data is rejected at this time, only remaining noise data, passes through structure constraint formula later
Calculate amplitude and phase error correction matrix T, the expression formula of the constraint formula are as follows:
In formula, h=[1,0,0 ..., 0]1×MN, hta=1 indicates first array element of Virtual array to be reference array element, by
In projection matrixFor orthogonal intersection cast shadow matrix, therefore projection matrixNot only meet Hermite condition, also meets idempotent item
Part, soThen constraining formula variation is the first constraint formula, i.e., formula 26 is transformed to formula 27, the first constraint formula
Expression formula are as follows:
Later, in order to acquire amplitude and phase error correction matrix T, the element of the first constraint formula need to be converted, first by x
(l) diagonalization to be to become diagonal matrix, then X=diag (x (l)), then by the member in amplitude and phase error correction matrix T on diagonal line
Element extracts, be put into a dimension be the column vector of NK × 1 in, by dimension be NK × 1 column vector be denoted as t, then Τ x (l)=
Xt, then the first constraint formula variation is the second constraint formula, i.e. formula 27 is transformed to formula 28, the expression formula of the second constraint formula are as follows:
In formula, t and taRelationship beIt willIt is denoted as B, then the second constraint formula becomes
Third constraint formula is turned to, third constrains the expression formula of formula are as follows:
And it willIt is denoted as A, then the variation of third constraint formula is the 4th constraint formula, the expression formula of the 4th constraint formula
Are as follows:
The 4th constraint formula is solved using method of Lagrange multipliers, obtains column vector taAre as follows:
Column vector t is had been presented in formula 20aWith the relationship of amplitude and phase error correction matrix T, then when be calculated column
Vector taLater, by taBeing updated to formula 20 can be obtained by amplitude and phase error correction matrix T.
Step 5, the echo data x (l) received is corrected by formula 22 using amplitude and phase error correction matrix T,
Then in the operation for carrying out clutter recognition and target detection.
In the prior art, airborne bistatic MIMO radar amplitude and phase error correction method is solving amplitude and phase error correction matrix
When, it needs to calculate projection matrix using clutter plus noise covariance matrix, while adding in the calculating formula of correction matrix comprising clutter
Noise covariance matrix, and the estimation of clutter plus noise covariance matrix needs the data using multiple training units, training number
According to selection directly affect the effect of amplitude and phase error correction.And above scheme of the invention, it is no longer rely on clutter plus noise association side
Difference calculates projection matrix, but uses the geometrical model of airborne bistatic MIMO radar, passes through one distance of geometry calculation
Three-dimensional steering vector when the sky of all clutter scattering points, then calculates projection matrix using these steering vectors, simultaneously in door
Correction matrix only includes the reception data for needing to correct, and is compared with the traditional method, this method computational accuracy is higher, and increases
In non-homogeneous clutter environment stability inferior.
The bearing calibration of the embodiment of the present invention realizes the correction to amplitude phase error by the data of single range gate, is correcting
Clutter Orthogonal Subspaces complementary space projection matrix used in process is the geometry meter by airborne bistatic MIMO radar
It obtains, avoids influence of the echo data to projection matrix, calculating speed is greatly improved with counting accuracy, and this method is most
The data that single range gate has been only used in the correction matrix acquired eventually, avoiding the non-homogeneous bring of sample influences, and increases
The stability of amplitude and phase error correction improves the accuracy of amplitude and phase error correction.
Below by way of emulation experiment further illustrate the present invention it is above-mentioned the utility model has the advantages that
1, simulation parameter is arranged
Emulation experiment realizes that airborne bistatic MIMO radar system parameter is respectively set using Matlab Programming with Pascal Language are as follows:
Transmitter and receiver use the operating mode of positive side view, and transmitter is located at the due east direction of receiver, and baseline length is
100km, transmitter height are set as 10km, and transmitting array element number is 2, and transmitter velocity magnitude is 100m/s, receiver height
It is set as 10km, receiving array element number is 3, and receiver velocity magnitude is 100m/s, and coherent accumulation pulse number is 4, pulse
Repetition rate is 2000, and radar operation wavelength is 0.25m, and miscellaneous noise ratio 60dB, transmitter and receiver are all to direct north
Flight.
2, emulation content and analysis of simulation result
Experiment one: assuming that transmitter and receiver all deposits the amplitude phase error of array, wherein range error is in [- 0.2,0.2]
Within the scope of this, phase error is at [- 3 °, 3 °] within the scope of this, method and IAD-SR- that this experiment proposes the present embodiment
STAP method compares, wherein IAD-SR-STAP is a kind of compressed sensing based method, and this method is by the width phase of appearance
Error goes the amplitude phase error value of approaching to reality by continuous iteration as the disturbance term of perception matrix.Simulation result such as Fig. 4 and
Shown in Fig. 5, Fig. 4 is two methods to the comparison diagram of amplitude correction, the method that as can be seen from Figure 4 the present embodiment proposes with
IAD-SR-STAP can effectively correct range error, and the method for the present embodiment more approaching to reality value, Fig. 5 are
Estimation of the two methods to phasing, as can be seen from Figure 5 to the correction result of phase and to the correction result class of amplitude
Seemingly, two methods can effectively correct phase error, and the method correction accuracy of the present embodiment is higher.
Experiment two: in the case where all there is the amplitude phase error of array in transmitter and receiver, wherein range error [-
0.2,0.2] within the scope of this, phase error is at [- 3 °, 3 °] within the scope of this.Fig. 6 is to be corrected front and back to range error to change
Kind factor comparison diagram, as seen from Figure 6, due to the presence of array range error, so that the performance of space-time adaptive processing is big
The decline of amplitude, after correction process, the performance boost of space-time adaptive processing, but also deposited with without being compared when error
In a certain distance；Fig. 7 be phase error be corrected front and back improvement factor comparison diagram, it can be seen that there are phase error with deposit
In amplitude phase error, situation is similar, performance a sharp decline that the presence of error can all make space-time adaptive handle, then
By correcting so that the case where performance increases, but process performance is not present again below error, complex chart 6 and Fig. 7's
As a result, same it can be concluded that the correcting algorithm of this paper can be to the conclusion that amplitude phase error is effectively corrected.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above method embodiment can pass through
The relevant hardware of program instruction is completed, and program above-mentioned can be stored in a computer readable storage medium, the program
When being executed, step including the steps of the foregoing method embodiments is executed；And storage medium above-mentioned includes: ROM, RAM, magnetic disk or light
The various media that can store program code such as disk.
Obviously, various changes and modifications can be made to the invention without departing from essence of the invention by those skilled in the art
Mind and range；In this way, if these modification and variations of the invention belong to the range of the claims in the present invention and its equivalent technologies
Within, then the present invention is also intended to include these modifications and variations.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (4)
1. a kind of airborne bistatic MIMO radar amplitude and phase error correction method based on single range gate, which is characterized in that the machine
The transmitter for carrying bistatic MIMO radar is the even linear array for including M array element, and receiver is the uniform line for including N number of array element
Battle array, detection range are divided into L range gate, wherein M, N and L are positive integer, and described method includes following steps:
Step 1, the number of echoes of an airborne bistatic MIMO radar range gate l to be detected in detectable range is obtained
According to xl, l is 1 to an integer value between L, the echo data xlIn only include clutter information and noise information, and it is described
Echo data xlThere are the amplitude phase errors of array element；
Step 2, the range gate l is divided into NcA clutter scattering point, calculates the NcA clutter scattering point is relative to transmitter
Azimuth angle thetatAnd pitch angleThe NcAzimuth angle theta of a clutter scattering point relative to receiverrAnd pitch angleAccording to
The azimuth angle theta being calculatedt, the pitch angleThe azimuth angle thetarWith the pitch angleIt calculates each described miscellaneous
The normalization Doppler frequency f of wave dispersion exit pointd,i, normalized emission spatial frequency ft,iWith normalization reception space frequency fr,i, so
Afterwards according to the normalization Doppler frequency fd,i, the normalized emission spatial frequency ft,iWith the normalization reception space frequency
Rate fr,iThree-dimensional is oriented to column vector when calculating the sky of each clutter scattering point, later by the NcA clutter scattering point
Three-dimensional guide row vectorial structure is at a matrix when empty；
Step 3, N step 2 obtained using Schmidt orthogonalization methodcThree-dimensional guide row when the sky of a clutter scattering point
Vectorial structure at matrix be orthogonalized processing, obtain one group of orthogonal basis, calculating clutter subspace just using the orthogonal basis
Hand over the projection matrix of complementary space
Step 4, amplitude and phase error correction matrix T is set, using the amplitude and phase error correction matrix T to there are the receptions of amplitude phase error
Data xlIt is corrected processing, by the reception data x after correctionlWith the projection matrix of the clutter Orthogonal Subspaces complementary space
It is multiplied, using first array element of Virtual array as reference array element structure constraint condition, calculates the amplitude and phase error correction matrix
T；
Step 5, using the amplitude and phase error correction matrix T to the range error of airborne bistatic MIMO radar and phase error into
Row correction.
2. the method according to claim 1, wherein the echo data x of the step 1lExpression formula are as follows:
In formula, xcIndicate clutter data, N indicates noise data and sets noise as white Gaussian noise, ρiIndicate receive i-th
The echo size of a clutter scattering point, a (ft,i) indicate i-th of clutter scattering point normalized emission steering vector, b (fr,i) table
Show that the normalization of i-th of clutter scattering point receives steering vector, c (fd,i) indicate i-th of clutter scattering point normalization Doppler
Steering vector, s (ft,i,fr,i,fd,i) indicate three-dimensional steering vector when the sky of i-th of clutter scattering point.
3. the method according to claim 1, wherein the step 2 specifically comprises the following steps:
(2a) is according to the transmitter, the receiver and the NcAny one clutter scattering point P's in a clutter scattering point
Coordinate information calculates separately the spacing R of the clutter scattering point P and transmittertWith the spacing R of receiverr, the clutter scattering point
The spacing R of P and the transmittertWith the spacing R of the clutter scattering point P and the receiverrExpression formula be respectively as follows:
In formula, the coordinate of the transmitter is denoted as (xt,yt,zt), the coordinate of the receiver is denoted as (xr,yr,zr), it will be described
The coordinate of clutter scattering point P is denoted as (xP,yP,0)；
According to the transmitter, the receiver and the NcThe coordinate of any one clutter scattering point P in a clutter scattering point
Information and the spacing RtWith spacing RrCalculate the azimuth angle theta of the clutter scattering point P and the transmittertAnd pitch angleThe azimuth angle theta of the clutter scattering point P and the receiverrAnd pitch angleThe azimuth angle thetat, the pitch angleThe azimuth angle thetarWith the pitch angleExpression formula be respectively as follows:
(2b) is according to the azimuth angle thetat, the pitch angleThe azimuth angle thetarWith the pitch angleCalculate the clutter
The normalization Doppler frequency f of scattering point Pd,i, normalized emission spatial frequency ft,iAnd normalization reception space frequency fr,i,
The normalization Doppler frequency fd,i, the normalized emission spatial frequency ft,iWith the normalization reception space frequency fr,i
Expression formula be respectively as follows:
(2c) is according to the normalized emission spatial frequency ft,iObtain emission space steering vector a (ft,i), according to the normalizing
Change reception space frequency fr,iObtain reception space steering vector b (fr,i), according to the normalization Doppler frequency fd,iIt obtains more
General Le steering vector c (fd,i), the emission space steering vector a (ft,i), the reception space steering vector b (fr,i) and institute
State Doppler steering vector c (fd,i) expression formula be respectively as follows:
(2d) calculates the emission space steering vector a of each clutter scattering point according to step (2a)~(2c)
(ft,i), the reception space steering vector b (fr,i) and Doppler's steering vector c (fd,i), and according to miscellaneous described in each
The emission space steering vector a (f of wave dispersion exit pointt,i), the reception space steering vector b (fr,i) and the Doppler lead
To vector C (fd,i) three-dimensional steering vector when the sky of each clutter scattering point is obtained, three-dimensional steering vector when described empty
Expression formula are as follows:
In formula, s (ft,i,fr,i,fd,i) indicate three-dimensional steering vector when the sky of i-th of clutter scattering point；
Later by the NcThree-dimensional guide row vectorial structure is at a matrix when sky of a clutter scattering point.
4. according to the method described in claim 3, it is characterized in that, the step 4 specifically comprises the following steps:
Emission array amplitude phase error is defined as e by (4a)t, the expression formula of emission array amplitude phase error are as follows:
et=[ρt,1,ρt,2..., ρt,M]T
In formula, ρt,iAmplitude phase error existing for i-th of transmitting array element of expression, i=1,2 ..., M, andWherein,
γt,iIndicate range error existing for i-th of transmitting array element, ξt,iIndicate phase error existing for i-th of transmitting array element；
Receiving array amplitude phase error is defined as er, it is expressed by following formula:
er=[ρr,1,ρr,2..., ρr,N]T
In formula, ρr,iI=1,2 ..., N indicate amplitude phase error existing for i-th of reception array element,Wherein, γr,iTable
Show range error existing for i-th of reception array element, ξr,iIndicate phase error existing for i-th of reception array element；
At this point, emission space guiding becomesWherein Γet=diag (et) indicate the width phase of emission array
Error etDiagonal matrix is pulled into, reception space steering vector becomesWherein, Γer=diag (er) indicate
By the amplitude phase error e of receiving arrayrPull into diagonal matrix；
Three-dimensional steering vector becomes when receiving the sky of data:
(4b) sets the amplitude and phase error correction matrix T of the airborne bistatic MIMO radar array element, the amplitude and phase error correction square
Battle array T meets relational expression Τ=Γ-1, according to the relational expression to Γ, the expression formula of the amplitude and phase error correction matrix T are as follows:
In formula, column vector taIn element and the emission array amplitude phase error etElement and the receiving array width phase
Error erElement correspond, the column vector taEach of element be the emission array amplitude phase error etAnd institute
State the amplitude phase error e of receiving arrayrIn each corresponding element inverse, the column vector taExpression formula are as follows:
In formula, 1MN×1It indicates the column vector that MN × 1 is tieed up and whole elements is that 1, Θ is indicated the amplitude phase error e of the emission arrayt
With the amplitude phase error e of the receiving arrayrIn each corresponding element be divided by；
The amplitude and phase error correction matrix T is multiplied to obtain with the data x (l) there are error:
Τ x (l)=Τ Γ xc(l)+Τ N=xc(l)+ΤN
In formula, xc(l) clutter data is indicated, N indicates noise data；
Set space CnBy L and M, the two subspaces are constituted, in space CnIn have any x ∈ Cn, and Unique Decomposition of Ring are as follows:
X=y+z y ∈ L, z ∈ M
In formula, y indicates x along the projection of M to L；
Set projection operator PL,M, the projection operator PL,MExpression formula be shown below:
PL,MX=y
In formula, projection operator PL,MIndicate by any x along M to L progress projective transformation, if x in the L of subspace, then PL,MX=
X, if x in the M of subspace, then PL,MX=0；
Set the projection matrix of the clutter Orthogonal Subspaces complementary spaceThe then projection matrixWith clutter data xc
(l) being multiplied is 0, i.e.,Then by the projection matrixThe amplitude and phase error correction matrix T and described
There are the data x (l) of error multiplications, obtain following expression:
The amplitude and phase error correction matrix T, the expression formula of the constraint formula are calculated by structure constraint formula later are as follows:
In formula, h=[1,0,0 ..., 0]1×MN, hta=1 indicates that by first array element of Virtual array be reference array element, by institute
State projection matrixFor orthogonal intersection cast shadow matrix, therefore the projection matrixNot only meet Hermite condition, also meets power
Etc. conditions, soThen the constraint formula variation is the first constraint formula, the expression formula of the first constraint formula
Are as follows:
Later, first by x (l) diagonalization to become diagonal matrix, then X=diag (x (l)), then by the amplitude phase error school
Element extraction in positive matrices T on diagonal line comes out, and it is NK × 1 by the dimension that being put into a dimension, which is in the column vector of NK × 1,
Column vector be denoted as t, then Τ x (l)=Xt, then the first constraint formula variation is the second constraint formula, the second constraint formula
Expression formula are as follows:
In formula, t and taRelationship beIt willIt is denoted as B, then the second constraint formula becomes
Turn to third constraint formula, the expression formula of the third constraint formula are as follows:
And it willIt is denoted as A, then the third constraint formula variation is the 4th constraint formula, the expression of the 4th constraint formula
Formula are as follows:
The 4th constraint formula is solved using method of Lagrange multipliers, obtains column vector taAre as follows:
According to the column vector taWith the relationship of the amplitude and phase error correction matrix T, the amplitude and phase error correction matrix T is obtained.
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