CN109358328A - The polar coordinates format image-forming method of the bistatic Forward-looking SAR of motor platform - Google Patents
The polar coordinates format image-forming method of the bistatic Forward-looking SAR of motor platform Download PDFInfo
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Abstract
The present invention discloses a kind of polar coordinates format image-forming method of bistatic forward sight spot beam SAR of motor platform, using the method for wave-number spectrum supporting domain affine transformation, the parallelogram wave-number spectrum supporting domain of MP-BFSAR is transformed to horizontal quasi rectangle, then the resampling for realizing wave-number spectrum distance to polar coordinates to rectangular co-ordinate is converted to chirp-z by distance, Range compress and scene center motion compensation are carried out later, then the resampling of wave-number spectrum orientation polar coordinates to rectangular co-ordinate is realized using the method for rising sampling mapping accumulation in orientation；Then two-dimentional inverse Fourier transform is carried out, thick imaging results are obtained；Final imaging results are obtained finally by defocus correction；The utilization rate of wave-number spectrum collected by the present invention is significantly improved compared to existing method.
Description
Technical Field
The invention belongs to the field of Bistatic Forward-looking synthetic aperture Radar (BFSAR) imaging, and particularly relates to a polar coordinate format algorithm of a Bistatic Forward-looking beamforming synthetic aperture Radar of a motorized platform.
Background
Due to the spatial separation of the transmitting station and the receiving station, the bistatic SAR breaks through the forward-looking constraint of the SAR, so that the receiving platform can image forward-looking terrain in the flight direction, and the unique characteristic enables the BFSAR to be a sensing technology with a very promising prospect. BFSAR is capable of providing full-time, all-weather forward-looking high resolution images.
Due to its bistatic forward-looking configuration, the echo of the MP-BFSAR exhibits severe two-dimensional spatial error, its wavenumber spectrum support region is usually a parallelogram rather than a rectangle, and thus it is difficult to effectively use the collected wavenumber spectrum; since MP-BFSAR beams are usually operated in a mode intended to continuously obtain high resolution images of the region of interest in many applications, this leads to complex time-frequency characteristics of the echoes, such as doppler aliasing.
The PFA algorithm (Parabola fitting algorithm) processes echoes in k-space (i.e. the wave number domain). PFA is suitable for processing SAR data due to its unique characteristics, such as mode-free doppler aliasing, low platform trajectory limitation, and low computational complexity. PFA is currently widely used in monostatic SAR and bistatic SAR.
Since PFA adopts the plane wave assumption, but there is a curve in the actual wavefront, when the imaging scene is large, the wavefront curve correction is needed, which may be ineffective for large scenes.
The documents "Polar format algorithm for bistatic SAR, IEEE trans. aerosol. electron. syst., vol.40, No.4, pp.1147-1159, oct.2004" and "Space-variable filtering for wave front geometry in Polar equation SAR image, IEEE trans. aerosol. electron.syst., vol.48, No.2, pp.940-950, apr.2012" propose methods of k-Space axis rotation to transform the spectral support domain of a tilted parallelogram into a horizontal parallelogram, however, k-Space axis rotation is only valid if the support region is rectangular or quasi-rectangular. Therefore, it is not suitable for MP-BFSAR in which the support area is a parallelogram; in the document "Polar format algorithm wave front reconstruction under the array radar flight path, IEEE geosci. remotesens. lett., vol.9, No.3, pp.526-530, May 2012", in order to compensate for phase errors caused by wavefront bending, a space variant wavefront bending compensation filter is proposed, which exploits the intrinsic isotropic property of Polar to cartesian resampling operations, however, the space variant wavefront bending compensation filter is implicit, the calculation of which involves two-dimensional interpolation, which means that it is inconvenient and inefficient in practice; in the documents "Space-variant filtering for wave front curvature in polar formed bistatic SAR image, ieee trans a.
Disclosure of Invention
In order to solve the technical problem, the invention provides a polar coordinate format imaging method of a bistatic forward-looking SAR of a motorized platform.
The technical scheme adopted by the invention is as follows: a polar coordinate format imaging method of a bistatic forward-looking SAR (synthetic aperture radar) of a mobile platform adopts a wave number spectrum support domain affine transformation (KAM) method, converts a parallelogram wave number spectrum support domain of an MP-BFSAR into a horizontal quasi-rectangle, then realizes resampling of a wave number spectrum distance from a polar coordinate to a rectangular coordinate through distance-to-Z transformation (CZT), then performs distance compression and scene center motion compensation, and then realizes resampling of a wave number spectrum orientation from the polar coordinate to the rectangular coordinate by adopting an Upsampling Mapping Accumulation (UMA) method in an orientation direction; then, two-dimensional Inverse Fourier transform (IFFT) is carried out to obtain a coarse imaging result; and finally, obtaining a final imaging result through defocusing correction.
Affine transform (KAM) of wave number spectrum, which comprises the following steps:
a1, calculating echo delay gradient;
a2, calculating the echo Doppler gradient;
a3, calculating an affine matrix and an inverse matrix thereof according to the echo delay gradient and the echo Doppler gradient;
a4, calculating wave numbers in the directions of an x coordinate and a y coordinate;
a5, calculating the distribution range of KAM back wave number according to the wave number in the directions of the x coordinate and the y coordinate and the affine matrix;
and A6, calculating the coordinate range of the image according to the wave number distribution range and the inverse matrix of the affine matrix.
The resampling from a polar coordinate to a rectangular coordinate of the wave number spectrum distance direction is realized by the distance direction CZT; the method specifically comprises the following steps:
b1, modeling an echo signal;
b2, performing distance direction CZT on the echo signal modeled in the step B1;
the azimuth up-sampling mapping accumulation specifically comprises the following processes:
c1, up-sampling the azimuth direction of the signal obtained in the step B2 by NuDoubling;
and C2, performing azimuth signal accumulation on the signals after the step C1.
Azimuth signal accumulation
C2, calculation from η Axis to kqMapping relation of the axes;
and C3, accumulating the signals obtained in the step C1 according to the mapping relation of the step C2.
And obtaining a final imaging result through defocus correction, and specifically comprising the following processes:
d1, calculating a phase error caused by wavefront curvature;
d2, calculating and calculating a secondary phase error caused by wavefront bending according to the phase error of the step D1;
d3, constructing a defocus correction filter according to the secondary phase error;
d4, dividing the coarse imaging result into a plurality of sub-images;
d5, multiplying the sub-images by the defocus correction filter constructed in the step D3 to perform defocus correction;
d6, splicing all the sub-images after defocusing correction obtained in the step D5 to obtain a final imaging result.
The invention has the beneficial effects that: the method of the invention adopts KAM method to transform the wave number spectrum support domain of the parallelogram to the horizontal quasi-rectangle, so that the utilization rate of the collected wave number spectrum is improved by about 60 percent; because both CZT and UMA can be efficiently realized through Fast Fourier Transform (FFT), IFFT and phase multiplication, the PFA provided by the invention is more efficient; compared with the conventional numerical filter, the analytic defocus correction filter provided by the invention is more convenient and efficient, and the PFA algorithm can be suitable for a large imaging scene through defocus correction of the invention.
Drawings
FIG. 1 is a flow chart of an imaging process of the method of the present invention;
FIG. 2 is a bistatic SAR echo recording geometric model of the mobile platform according to the present invention;
FIG. 3 is a wavenumber spectrum support domain before and after KAM;
wherein FIG. 3(a) is the wavenumber spectrum support domain before KAM; FIG. 3(b) is a wavenumber spectrum support domain after KAM;
FIG. 4 is an imaging result of a point target;
FIG. 5 is an enlarged isometric view of the point target imaging results of FIG. 4;
fig. 6 is an imaging result of a planar target.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to the accompanying drawings.
Fig. 1 shows a flow chart of the scheme of the invention, which comprises the following steps: transforming a parallelogram wave number spectrum support domain of the MP-BFSAR into a horizontal quasi-rectangle by adopting a wave number spectrum support domain affine transformation (KAM), then realizing resampling from a distance direction polar coordinate to a rectangular coordinate by a distance direction-Z transformation (CZT), then performing distance compression and scene center motion compensation, and realizing resampling from a polar coordinate to the rectangular coordinate of a wave number spectrum orientation by adopting a Upsampling Mapping Accumulation (UMA) method in the orientation direction; then, two-dimensional Inverse Fourier transform (IFFT) is carried out to obtain a coarse imaging result; and finally, obtaining a final imaging result through defocusing correction.
The method specifically comprises the following 5 steps:
1. wave number spectrum affine transform (KAM):
a1, echo delay gradient of
Where, c represents the speed of light,respectively representing the unit vectors, r, of the directions of the sight lines from the transmitting station and the receiving station to the scene center at the azimuth zero timeT0＝(xT,yT,zT)、rR0＝(xR,yR,zR) Position vectors, R, representing the transmitting and receiving stations at the initial time, respectivelyT0＝|rT0|、RR0＝|rR0And | respectively represents the distance from the transmitting station and the receiving station to the scene center at the azimuth zero moment.
The projection of the time delay gradient on the ground is
Ggτ＝PGτ
Wherein,representing a ground projection matrix.
A2, calculating Doppler gradient
Echo Doppler gradient of
Where λ denotes the carrier wavelength, vT＝(vTx,vTy,vTz)、vR＝(vRx,vRy,vRz) Respectively, the velocity of the transmitting station and the receiving station at the azimuth zero time, and I represents an identity matrix.
The projection of the Doppler gradient on the ground is
Ggd＝PGd
A3, calculating affine matrix and inverse matrix thereof
Wherein, denotes the angle, phi, between the vector direction and the positive direction of the horizontal axisc＝|θgd-θgτAnd | represents the coupling angle of the wavenumber spectrum.
Inverting affine matrix
A4, calculating wave number in x coordinate and y coordinate directions
ΔR(η；x,y)＝Rbi(η；x,y)-Rbi(0; x, y) represents the differential distance, and a first order Taylor approximation is made to the differential distance:
ΔR(η；x,y)＝RSAG(η；x,y)-RSAG(0；x,y)≈C10x+C01y，
wherein
Obtaining the projection of the wave number k on the x axis and the y axis as kx＝kC10,ky＝kC01Wherein
k＝2π(fr+fc)/c
That is, the wave numbers in the x-coordinate and y-coordinate directions are respectively
kx＝kC10
ky＝kC01
Rbi(η；x,y)＝RT(η；x,y)+RR(η; x, y) denotes bistatic distance and, η denotes slow time,
RT(η；x,y)、RR(η; x, y) denotes the distance history of the transmitting and receiving stations, respectively, aT＝(aTx,aTy,aTz)、aR＝(aRx,aRy,aRz) Representing the accelerations of the transmitting and receiving stations, r, respectivelyPAnd (x, y,0) represents the position coordinates of any point object in the scene.
A5 calculating the distribution range of KAM wave number
Wherein k isxmin,kxmaxRespectively represents kxMinimum and maximum values of, kymin,kymaxRespectively represents kyMinimum and maximum values of;
KAM back distance wavenumber variable kpHas a distribution range of [ k ]pmin,kpmax]Wherein
kpmin＝min{kp1,kp2,kp3,kp4}
kpmax＝max{kp1,kp2,kp3,kp4}
KAM rear azimuth wave number variable kqHas a distribution range of [ k ]qmin,kqmax]Wherein
kqmin＝min{kq1,kq2,kq3,kq4}
kqmax＝max{kq1,kq2,kq3,kq4}
A6, calculating the coordinate range of the output image, specifically as follows:
wherein x ismin,xmaxMinimum and maximum values, y, respectively representing the abscissa of the original scenemin,ymaxRespectively representing the minimum value and the maximum value of the ordinate of the original scene;
the distance-to-coordinate range of the output image is [ p ]min,pmax]Wherein
pmin＝min{p1,p2,p3,p4}
pmax＝max{p1,p2,p3,p4}
The azimuth coordinate range of the output image is [ q ]min,qmax]Wherein
qmin＝min{q1,q2,q3,q4}
qmax＝max{q1,q2,q3,q4}
2. Distance direction CZT:
b1 echo signal modeling
The range frequency domain azimuth baseband echo can be modeled as follows
Wherein, KrDenotes the emission pulse modulation frequency, τ denotes the fast time, c denotes the speed of light, and λ denotes the carrier wavelength.
B2, distance direction CZT
Finding the frequency spectrum of the echo at the position below the complex plane unit circle by the distance direction CZT to the echo signal
zi＝exp{j(φ0+iΔφ)},i＝0,1,2,...,Np
Wherein,
wherein, FsFor the sampling rate of the fast time t,denotes the magnitude of the center wave number, kpmin、kpmaxRespectively represents kpMaximum and minimum values of, NpIn order to output the distance of the image to the number of sampling points, the value of the distance must satisfy the following conditions:
the distance direction CZT signal can be expressed as
Wherein k ispThe distance after KAM is expressed as a variable in wavenumber.
3. Matched filtering (MF, Match filter) and scene center motion compensation (MoCo to SC), i.e. multiplying the distance to CZT result by the following phase function:
the signals after MF and MoCo to SC can be approximately expressed as
Wherein p and q represent distance direction and azimuth direction coordinate variables of the output image, respectively.
4. Azimuth up-sampling mapping accumulation:
c1, up-sampling the azimuth direction of the signal obtained in the step 3 by NuMultiplying, and recording the resulting signal as S3(kpη (m), p, q), where m denotes the sample number η after up-sampling
Wherein N isaNumber of samples, N, representing η before upsamplinguGenerally, the value is 4 or 8;
c2, calculation from η Axis to kqMapping relationship of axes:
wherein round {. } represents a rounding operation,represents kqSampling interval of the shaft;
c3, accumulation of azimuth signals
And accumulating the signals obtained by the C1 in the azimuth direction according to the mapping relation obtained by the C2:
wherein N, NqRespectively representing signals at kqSampling point number and number of sampling points of the shaft.
To this end, we obtainp,kq) A signal of a domain which can be approximately expressed as
S4(kp,kq；p,q)≈exp{-j(kpp+kqq)}
And C4, performing two-dimensional inverse Fourier transform (IFFT) on the signals obtained by the C3 to obtain a coarse imaging result.
5. For the case of a large scene, the defocus effect of the edge target caused by the wavefront curvature is not negligible, and the defocus correction needs to be performed on the coarse imaging result:
d1, calculating the phase error caused by the wave front bending, specifically as follows:
the phase error caused by the wavefront curvature is
ΦWC(k,η；x,y)＝-kΔR(η；x,y)+kxx+kyy
D2 calculating the secondary phase error caused by wave front bending
The quadratic phase error caused by wavefront curvature is calculated by implicit function theorem and complex function derivation method
D3 construction of defocus correction filter
D4, sub-picture division
Dividing coarse imaging results into N along q-axissubSub-images, each sub-image being transformed to (p, k) by Fast Fourier Transform (FFT) on qq) Domain of which NsubA positive integer satisfying the following formula
Wherein q ismSolved by the following equation
D5 sub-image defocus correction
Multiplying each sub-image by the following defocus correction filter
HRF(kq；p,qc)＝exp{-jk2D(p,qc)}
Wherein q iscAs the q-axis coordinate of the center of the sub-image, and then proceed with respect to kqThe (p, q) domain, and the defocus-corrected sub-image.
D6, subimage stitching
All defocus-corrected sub-images obtained at D5 were combined to obtain the final imaging result.
The technical effects of the present invention will be described below with reference to specific data.
As shown in table 1, the system parameters adopted in this embodiment are shown, and fig. 2 is a schematic diagram of the geometric configuration of the mobile bistatic SAR in this embodiment, it is assumed that there are 49 point targets uniformly distributed on the ground, and the distances between the point targets on the x-axis and the y-axis are both 800 meters.
TABLE 1 System parameters
Each item of calculation is performed based on the system parameter values in table 1, specifically:
the echo delay gradient calculation result is as follows:
the projection of the time delay gradient on the ground is: ggτ＝PGτ＝1.0×10-8[-0.2711,0.2634]T
The echo doppler gradient calculation result is:
the projection of the doppler gradient on the ground is: ggd＝PGd＝[-0.0001,0.0458]T
The coupling angle calculation results are:
φc＝|θgτ-θgd|＝45.7°
the affine matrix is:
and (3) inverting the affine matrix to obtain:
the wave number spectrum is affine transformed as follows
Magnitude of center wave number
kpThe maximum and minimum calculation results are:
kpmin＝28.38rad/m、kpmax＝30.99rad/m，
the number of distance-direction sampling points of the output image is as follows: n is a radical ofp＝3328。
NuThe sampling number of η after upsampling is 8:
the pulse repetition interval is: PRI 1/PRF 4ms,
signal at kqThe number of sampling points on the axis is: n is a radical ofq＝2224，
In addition, from kqmax＝-0.9044rad/m，kqmax0.8413rad/m, yield kqThe sampling interval of the shaft is
Signal at kqThe sampling number of the shaft is:
dividing the coarse focus map into N along the q-axissub8 sub-images and transform each sub-image to (p, k) by FFT with respect to qq) A domain;
the defocus correction filter is:
wherein D (p, q)c)＝7.31×10-6p2+1.02×10-5pqc+1.03×10-5q2，
p∈[-4.0020×103,3.9996×103]m；qcThe q-axis coordinate corresponding to the center of each sub-image has the value set of [ -3500, -2500, -1500, -500,500,1500,2500,3500 [ ]]m；
Obtaining simulation images shown in fig. 3, 4, 5 and 6 according to the calculation results; the simulation results of the wave number spectrum support domain before and after KAM are shown in fig. 3, and after KAM, the utilization efficiency of the wave number spectrum support domain of the point target is increased from 33% to 98%, so that the method provided by the invention can effectively improve the utilization efficiency of the wave number spectrum. The point target imaging results of the present invention are shown in FIG. 4; the corresponding amplified contour map of the point target imaging result is shown in fig. 5, and it can be seen that the contour map of the point target imaging result is uniformly and regularly distributed, and the Peak Side Lobe Ratio (PSLR) and the Integral Side Lobe Ratio (ISLR) are very close to theoretical values of-13.26 dB and-9.96 dB, which shows that the algorithm provided by the invention has good focusing imaging effect on the point target echo; the imaging result of the surface target is shown in fig. 6, and the surface target can be seen to be clear and distinguishable in fig. 6, which shows that the focusing imaging effect of the echo of the surface target by the algorithm provided by the invention is good. It can be seen from fig. 4, fig. 5 and fig. 6 that the method provided by the invention can effectively perform focusing imaging on the bistatic forward-looking SAR target echo of the mobile platform.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (7)
1. A polar coordinate format imaging method of a bistatic forward-looking beam-bunching synthetic aperture radar of a maneuvering platform is characterized in that,
firstly, transforming a parallelogram wave number spectrum support domain of the MP-BFSAR into a horizontal quasi-rectangle through wave number spectrum affine transformation; secondly, resampling the wave number spectrum distance from polar coordinates to rectangular coordinates by distance-to-chirp-z conversion; thirdly, performing distance compression and scene center motion compensation; resampling from the second, wave number spectrum azimuth to polar coordinate to rectangular coordinate; then, performing two-dimensional inverse Fourier transform to obtain a coarse imaging result; and finally, obtaining a final imaging result through defocus correction.
2. The polar coordinate format imaging method of the maneuvering platform bistatic forward-looking SAR as recited in claim 1, characterized in that the wave number spectrum affine transformation specifically comprises the following procedures:
a1, calculating echo delay gradient;
a2, calculating the echo Doppler gradient;
a3, calculating an affine matrix and an inverse matrix thereof according to the echo delay gradient and the echo Doppler gradient;
a4, calculating wave numbers in the directions of an x coordinate and a y coordinate;
a5, calculating the distribution range of KAM back wave number according to the wave number in the directions of the x coordinate and the y coordinate and the affine matrix;
and A6, calculating the coordinate range of the image according to the wave number distribution range and the inverse matrix of the affine matrix.
3. The polar format imaging method of the mobile platform bistatic forward-looking SAR of claim 2, wherein the distance-to-CZT implementation of wavenumber spectral distance-to-polar to rectangular re-sampling; the method specifically comprises the following steps:
b1, modeling an echo signal;
b2, performing distance direction CZT on the echo signal modeled in the step B1.
4. The polar coordinate format imaging method of the mobile platform bistatic forward-looking SAR as claimed in claim 3, wherein the resampling from polar coordinates to rectangular coordinates of wavenumber spectral azimuth is specifically as follows: adopting up-sampling mapping accumulation in the azimuth direction; the method comprises the following steps:
c1, up-sampling the azimuth direction of the signal obtained in the step B2 by NuDoubling;
and C2, performing azimuth signal accumulation on the signals after the step C1.
5. The powered platform bistatic forward-looking SAR pole of claim 4The coordinate format imaging method is characterized in that the signals after the step C1 are: s3(kp,η(m)；p,q)；
Wherein k ispRepresenting distance-direction wave number variables after affine transformation in a wave number spectrum support domain, η representing slow time, p representing distance-direction coordinates of an image, q representing azimuth-direction coordinates of the image, and m representing sampling sequence numbers after up-sampling η.
6. The polar coordinate format imaging method of the mobile platform bistatic forward-looking SAR as claimed in claim 5, wherein the azimuth signal accumulation is specifically:
first, calculate from η Axis to kqMapping relation of the axes;
then, the signals obtained in step C1 are accumulated according to the mapping relationship.
7. The polar coordinate format imaging method of the maneuvering platform bistatic forward-looking SAR as recited in claim 6, characterized in that the final imaging result is obtained by defocus correction, which specifically includes the following procedures:
d1, calculating a phase error caused by wavefront curvature;
d2, calculating a secondary phase error caused by the wave front bending according to the phase error of the step D1;
d3, constructing a defocus correction filter according to the secondary phase error;
d4, dividing the coarse imaging result into a plurality of sub-images;
d5, multiplying the sub-images by the defocus correction filter constructed in the step D3 to perform defocus correction;
d6, splicing all the sub-images after defocusing correction obtained in the step D5 to obtain a final imaging result.
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