CN110221295B - Imaging method for compensating frequency modulation continuous wave circular SAR intra-pulse motion - Google Patents

Imaging method for compensating frequency modulation continuous wave circular SAR intra-pulse motion Download PDF

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CN110221295B
CN110221295B CN201910523793.8A CN201910523793A CN110221295B CN 110221295 B CN110221295 B CN 110221295B CN 201910523793 A CN201910523793 A CN 201910523793A CN 110221295 B CN110221295 B CN 110221295B
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付耀文
张健丰
张文鹏
杨威
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National University of Defense Technology
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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
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    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth
    • 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
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    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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    • G01S13/9011—SAR image acquisition techniques with frequency domain processing of the SAR signals in azimuth

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Abstract

The invention belongs to the technical field of synthetic aperture radar imaging, and discloses an imaging method for compensating intra-pulse motion of a frequency-modulated continuous wave circular SAR (synthetic aperture radar). The invention adds a judgment process only related to parameters of a frequency-modulated continuous wave circular SAR imaging system in the imaging process to quickly judge whether the intra-pulse motion of the system can be ignored in the time domain method imaging process, and guides to select a proper imaging method. The invention solves the problems that stop-go-stop approximation is not effective any more and intra-pulse motion can not be ignored in the time domain method imaging process of the frequency modulation continuous wave circular SAR imaging system, and realizes high-efficiency high-resolution imaging of the frequency modulation continuous wave circular SAR time domain method.

Description

Imaging method for compensating frequency modulation continuous wave circular SAR intra-pulse motion
Technical Field
The invention belongs to the technical field of Synthetic Aperture Radar (SAR) imaging, and relates to an imaging method for compensating the intra-pulse motion of a frequency-modulated continuous wave circular SAR in an SAR time domain imaging method.
Background
The circular SAR takes the center of an observed scene as a circle center, makes circular motion around the observed scene at a certain fixed height above the scene, and in the process, a radar beam always points to the observed scene at a specific depression angle and acquires observed scene data. The circular SAR is used as a new imaging mode, a target azimuth spectrum is widened through aperture accumulation of 360 degrees, and under an ideal condition, the image resolution can reach a sub-wavelength order; meanwhile, the circular SAR platform does circular motion to form a two-dimensional synthetic aperture, so that the three-dimensional SAR platform has three-dimensional imaging capability. An imaging system combining frequency modulation continuous wave technology and a circumferential SAR not only has sub-wavelength high resolution and three-dimensional imaging capability, but also has incomparable advantages of pulse strip SAR such as small volume, light weight, low cost and the like. The frequency modulation continuous wave circular SAR can provide high-resolution images for battlefield situation analysis, reconnaissance evaluation, resource exploration, terrain exploration, disaster prediction and evaluation and the like, and has wide application prospects in the fields of military affairs and civil affairs.
Although frequency modulated continuous wave circular SAR has great potential in high resolution imaging, there are still great challenges to exploiting these potentials. Aiming at the particularity of the circular SAR motion trail, a comparison file' Chenoppin, airborne circular synthetic aperture radar imaging technology research [ D ]. Changsha: a doctoral paper of the university of defense science and technology, 2018, "proposes a Back Projection (BP) method suitable for circumferential SAR imaging. The method is very suitable for circular SAR imaging due to high imaging precision, simple imaging processing process and no limitation of SAR motion trail. However, the time domain BP method is based on a pulse system, that is, the pulse duration is very short, the stop-go-stop approximation is adopted instead of the walk of the intra-pulse platform, if the BP method is still adopted to image the frequency-modulated continuous wave circular SAR which can ignore intra-pulse motion, an imaging result with better quality can be obtained, however, if the BP method is also adopted to image the frequency-modulated continuous wave circular SAR which cannot ignore intra-pulse motion, the distance offset error introduced by intra-pulse motion cannot be compensated, and a high-resolution image cannot be obtained, and the time domain method can simply and directly rapidly determine whether the influence of intra-pulse motion on the imaging result can be ignored in the imaging process due to the fact that no judgment process exists, so that the imaging of the frequency-modulated continuous wave circular SAR time domain method cannot be rapidly implemented.
Disclosure of Invention
The invention aims to provide an imaging method for compensating the intra-pulse motion of a frequency-modulated continuous wave circular SAR (synthetic aperture radar), namely an improved time domain BP (back propagation) method, aiming at the problems that stop-go-stop approximation is not effective any more and the intra-pulse platform motion can not be ignored in the imaging process of the frequency-modulated continuous wave circular SAR time domain method.
In order to achieve the purpose, the invention is realized by the following technical scheme:
an imaging method for compensating frequency modulation continuous wave circular SAR intra-pulse motion specifically comprises the following steps:
the method comprises the following steps of 1, acquiring frequency modulation continuous wave circular SAR echo signals, initializing parameters of a frequency modulation continuous wave circular SAR imaging system and modeling the frequency modulation continuous wave circular SAR echo signals, wherein the method is based on the following steps:
(1.1) initializing parameters of a frequency modulation continuous wave circular SAR imaging system: the radius of a circular motion track of the radar platform is R, the height is H, the azimuth observation angle is theta, and the phase center position A of the radar antenna is (x)r,yrH), wherein xr、yrAnd H are the x-axis, y-axis, and z-axis coordinates of position A, respectively, which may also be expressed as (Rcos θ, Rsin θ, H); the radius of the circular observation scene of the ground plane is RaThe coordinates of any point object P in the scene are (x, y,0), and can also be expressed as
Figure GDA0002764024570000021
Wherein r and
Figure GDA0002764024570000022
respectively the radial radius and azimuth angle of the target P; the radar motion angular speed is omega, the vehicle speed V is R omega, the azimuth observation angle corresponding to t time is theta t, and the full time
Figure GDA0002764024570000023
Wherein t ismWhich indicates a slow time in which the time,
Figure GDA0002764024570000024
the time is fast;
(1.2) modeling of a frequency modulation continuous wave circular SAR echo signal: instantaneous slope distance R between radar position A and target PrComprises the following steps:
Figure GDA0002764024570000025
calculation of RrAt a fast time
Figure GDA0002764024570000026
The first order taylor expansion of (a) is:
Figure GDA0002764024570000027
wherein the content of the first and second substances,
Figure GDA0002764024570000028
Figure GDA0002764024570000029
Rcenthe instantaneous slope distance under the stop-go-stop approximation, namely the instantaneous slope distance of the pulse system circumference SAR,
Figure GDA00027640245700000210
a range migration error introduced for the intra-pulse motion of the frequency-modulated continuous wave circular SAR is also an error ignored by the pulse circular SAR;
when the radar emission signal is a chirp signal, the echo signal of the target P is:
Figure GDA00027640245700000211
where rect (-) is a rectangular window function, c is the speed of light, TpIs pulse duration, and
Figure GDA00027640245700000212
fcis a carrier frequency, KrFrequency-modulated, and Kr＝B/TpB is the bandwidth of a radar emission signal;
step 2, the line-breaking frequency modulation processing, the residual video phase elimination and the fundamental frequency echo signal acquisition are carried out based on the following steps:
(2.1) line-breaking tone processing: echo signal
Figure GDA00027640245700000213
And a reference signal
Figure GDA00027640245700000214
The difference frequency signal obtained by the conjugate multiplication of (a) is:
Figure GDA00027640245700000215
wherein the reference signal
Figure GDA00027640245700000216
Comprises the following steps:
Figure GDA00027640245700000217
Rreffor reference distance, take the instantaneous slope distance, R, between the target at the center of the scene and the radarΔ＝Rr-Rref(ii) a Last exponential term in difference frequency signal
Figure GDA0002764024570000031
Is a residual video phase term;
(2.2) residual video phase elimination and fundamental frequency echo signal acquisition: the difference frequency signal is subjected to distance Fourier transform and is compared with an exponential term exp (-j pi f)i 2/Kr) Multiplying to eliminate residual video phase, where fi＝-2KrRΔThe/c is the difference frequency, and then the difference frequency is subjected to inverse Fourier transform to obtain a fundamental frequency echo signal:
Figure GDA0002764024570000032
wherein λ ═ fcC is the carrier wavelength, RΔm＝Rcen-Rref；
Step 3, compressing the distance and analyzing the distance deviation error caused by the platform motion in the vein, based on the following steps:
(3.1) distance compression: the phase corresponding to the last exponential term of the fundamental frequency echo signal is
Figure GDA0002764024570000033
Wherein
Figure GDA0002764024570000034
Has a coefficient of
Figure GDA0002764024570000035
The maximum value is 4 pi B/2c and is in the millimeter wave band fc> B/2, 4 pi/lambda-4 pi fc/c > 4 π B/2c, i.e. exponential terms in the fundamental echo signal
Figure GDA0002764024570000036
Corresponding phase is much smaller than
Figure GDA0002764024570000037
And (3) neglecting the influence of the last exponential term in the fundamental frequency signal on imaging, and then carrying out Fourier transform along the distance direction to obtain a distance compression signal as follows:
Figure GDA0002764024570000038
(3.2) analyzing the distance deviation error caused by the intra-pulse motion: platform motion in range domain in frequency-modulated continuous wave circular SAR pulseThe frequency offset error caused is Δ fi＝-2k1λ, which is converted to a distance offset error of:
Figure GDA0002764024570000039
wherein, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a distance offset error Δ R1The maximum value of (a), namely the maximum distance offset error caused by the intra-pulse motion of the frequency-modulated continuous wave circular SAR to a certain target in the scene, is as follows:
Figure GDA00027640245700000310
in the above formula, let R ═ RaObtaining the maximum distance deviation error caused by the intra-pulse motion of the frequency modulation continuous wave circular SAR to the whole observation scene, and comparing the maximum distance deviation error with the theoretical plane resolution delta rho 'at the center of the frequency modulation continuous wave circular SAR scene'0The division yields a ratio of the maximum range offset error due to intra-pulse motion to the resolution of Δ C, where Δ ρ'0＝2.4λ/(4πcosθd0)，
Figure GDA00027640245700000311
The pitch angle of the frequency modulation continuous wave circumference SAR to the scene center target is shown, wherein delta C is as follows:
Figure GDA00027640245700000312
step 4, judging whether the intra-pulse motion can be ignored in the imaging process of the frequency modulation continuous wave circular SAR time domain method and guiding to select a proper imaging method: substituting parameters of a frequency modulation continuous wave circular SAR imaging system into an expression of delta C and calculating the value of delta C, when the distance offset error caused by intra-pulse motion of the frequency modulation continuous wave circular SAR is smaller than a distance resolution unit, namely the delta C is smaller than 1, neglecting the distance offset error caused by intra-pulse motion in the imaging process by adopting a frequency modulation continuous wave circular SAR time domain method, neglecting the intra-pulse motion at the moment, and imaging by adopting a pulse system circular SAR time domain method, namely obtaining a final frequency modulation continuous wave circular SAR image by adopting a time domain imaging method of stop-go-stop approximation; on the contrary, when the distance offset error caused by the frequency modulation continuous wave circular SAR intra-pulse motion is more than or equal to one distance resolution unit, namely delta C is more than or equal to 1, intra-pulse motion cannot be ignored in the imaging process by adopting the frequency modulation continuous wave circular SAR time domain method, at the moment, extra compensation needs to be carried out on the intra-pulse motion, the imaging method for compensating the frequency modulation continuous wave circular SAR intra-pulse motion is adopted for imaging, and the following steps are continued;
step 5, imaging scene grid division, namely dividing the radar observation scene into a plurality of unit grids with consistent sizes, wherein the size requirement of the unit grids is smaller than the theoretical plane resolution delta rho at the scene center0', i.e. Δ x' < Δ ρ0′，Δy′＜Δρ0', where Δ x ' and Δ y ' are the range-wise spacing and azimuth-wise spacing of the scene mesh, respectively;
step 6, calculating a new instantaneous slope distance R' of the grid point at a certain azimuth slow moment and including a distance offset error introduced by intra-pulse platform motion, and the specific steps are as follows:
calculating the instantaneous slope distance R of the grid point under the approximate stop-go-stop at the azimuth momentcenComprises the following steps:
Figure GDA0002764024570000041
calculating the distance deviation error Delta R of the platform motion in the pulse introduced in the distance domain1Comprises the following steps:
Figure GDA0002764024570000042
wherein, Δ fi＝-2k1The/lambda is the frequency offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse in a distance domain, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a new instantaneous slope distance R ═ Rcen+ΔR1；
Step 7, calculating the corresponding position of the distance compressed signal at the azimuth moment in the imaging grid according to the new instantaneous slope distance, namely projecting the distance compressed signal at the azimuth moment into the imaging grid according to the new instantaneous slope distance and recording as S'if(fi,tm)；
Step 8, azimuth phase compensation is carried out, and sub-images of a certain azimuth moment are obtained:
Figure GDA0002764024570000043
where x 'and y' are the grid coordinates in the scene, exp (j4 π R)Δm/λ) is an azimuth phase compensation function;
step 9, obtaining a final frequency modulation continuous wave circumferential SAR image, judging whether sub-images at all azimuth moments are obtained or not, namely whether sub-images at all sampling points in the azimuth direction are obtained or not, if not, entering the next azimuth moment and repeating the steps 6-8, and if sub-images at all azimuth moments are obtained, performing coherent superposition on the sub-images to obtain the final frequency modulation continuous wave circumferential SAR image:
Figure GDA0002764024570000044
wherein M is the number of sampling points in the azimuth direction in the whole 360-degree aperture.
Compared with the prior art, the invention has the following beneficial effects:
firstly, the judgment process in the time domain imaging method provided by the invention is only related to the parameters of the frequency modulation continuous wave circular SAR imaging system, and can be used for quickly judging whether the intra-pulse platform motion can be ignored or not in the time domain method imaging process of an actual frequency modulation continuous wave circular SAR imaging system, so as to guide the selection of a proper imaging method;
secondly, the time domain imaging method provided by the invention compensates the distance offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse, solves the problem that stop-go-stop approximation is not effective any more in the frequency modulation continuous wave circular SAR imaging process, realizes high-resolution imaging processing, and obtains a high-quality frequency modulation continuous wave circular SAR image.
Drawings
Fig. 1 is a general block diagram of an imaging method for compensating for intra-pulse motion of a frequency modulated continuous wave circular SAR of the present invention.
Detailed Description
In order to better explain the technical solution of the present invention, the following describes an embodiment of the present invention with reference to the accompanying drawings.
Fig. 1 is a general block diagram of an imaging method for compensating for intra-pulse motion of a frequency modulated continuous wave circular SAR of the present invention, which specifically includes the following steps:
the method comprises the following steps of 1, acquiring a frequency modulation continuous wave circular SAR echo signal, relating to parameter initialization of a frequency modulation continuous wave circular SAR imaging system and modeling of the frequency modulation continuous wave circular SAR echo signal, and based on the following steps:
(1.1) initializing parameters of a frequency modulation continuous wave circular SAR imaging system: the radius of a circular motion track of the radar platform is R, the height is H, the azimuth observation angle is theta, and the phase center position A of the radar antenna is (x)r,yrH), wherein xr、yrAnd H are the x-axis, y-axis, and z-axis coordinates of A, respectively, which may also be expressed as (Rcos θ, Rsin θ, H); the radius of the circular observation scene of the ground plane is RaThe coordinates of any point object P in the scene are (x, y,0), and can also be expressed as
Figure GDA0002764024570000051
Wherein r and
Figure GDA0002764024570000052
respectively the radial radius and azimuth angle of the target P; the radar motion angular speed is omega, the vehicle speed V is R omega, the azimuth observation angle corresponding to t time is theta t, and the full time
Figure GDA0002764024570000053
Wherein t ismWhich indicates a slow time in which the time,
Figure GDA0002764024570000054
the time is fast;
(1.2) modeling of a frequency modulation continuous wave circular SAR echo signal: instantaneous slope distance R between radar position A and target PrComprises the following steps:
Figure GDA0002764024570000055
calculation of RrAt a fast time
Figure GDA0002764024570000056
The first order taylor expansion of (a) is:
Figure GDA0002764024570000057
wherein the content of the first and second substances,
Figure GDA0002764024570000058
Figure GDA0002764024570000059
Rcenfor the instant slope distance under the stop-go-stop approximation,
Figure GDA00027640245700000510
introducing range migration errors for the frequency-modulated continuous wave circular SAR intra-pulse motion;
when the radar emission signal is a chirp signal, the echo signal of the target P is:
Figure GDA00027640245700000511
where rect (-) is a rectangular window function, c is the speed of light, TpIs pulse duration, and
Figure GDA00027640245700000512
fcis a carrier frequency, KrFrequency-modulated, and Kr＝B/TpB is the bandwidth of a radar emission signal;
step 2, the line-breaking frequency modulation processing, the residual video phase elimination and the fundamental frequency echo signal acquisition are carried out based on the following steps:
(2.1) line-breaking tone processing: echo signal
Figure GDA0002764024570000061
And a reference signal
Figure GDA0002764024570000062
The difference frequency signal obtained by the conjugate multiplication of (a) is:
Figure GDA0002764024570000063
wherein the reference signal
Figure GDA0002764024570000064
Comprises the following steps:
Figure GDA0002764024570000065
Rreffor reference distance, take the instantaneous slope distance, R, between the target at the center of the scene and the radarΔ＝Rr-Rref(ii) a Last exponential term in difference frequency signal
Figure GDA0002764024570000066
Is a residual video phase term;
(2.2) residual video phase cancellation and fundamental frequencyEcho signal acquisition: the difference frequency signal is subjected to distance Fourier transform and is compared with an exponential term exp (-j pi f)i 2/Kr) Multiplying to eliminate residual video phase, where fi＝-2KrRΔThe/c is the difference frequency, and then the difference frequency is subjected to inverse Fourier transform to obtain a fundamental frequency echo signal:
Figure GDA0002764024570000067
wherein λ ═ fcC is the carrier wavelength, RΔm＝Rcen-Rref；
Step 3, compressing the distance and analyzing the distance deviation error caused by the platform motion in the vein, based on the following steps:
(3.1) distance compression: the phase corresponding to the last exponential term of the fundamental frequency echo signal is
Figure GDA0002764024570000068
Wherein
Figure GDA0002764024570000069
Has a coefficient of
Figure GDA00027640245700000610
The maximum value is 4 pi B/2c and is in the millimeter wave band fc> B/2, 4 pi/lambda-4 pi fc/c > 4 π B/2c, i.e. exponential terms in the fundamental echo signal
Figure GDA00027640245700000611
Corresponding phase is much smaller than
Figure GDA00027640245700000612
And (3) neglecting the influence of the last exponential term in the fundamental frequency signal on imaging, and then carrying out Fourier transform along the distance direction to obtain a distance compression signal as follows:
Figure GDA00027640245700000613
(3.2) analyzing the distance deviation error caused by the intra-pulse motion: the frequency offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse in the distance domain is delta fi＝-2k1λ, which is converted to a distance offset error of:
Figure GDA00027640245700000614
wherein, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a distance offset error Δ R1The maximum value of (a), namely the maximum distance offset error caused by the intra-pulse motion of the frequency-modulated continuous wave circular SAR to a certain target in the scene, is as follows:
Figure GDA0002764024570000071
in the above formula, let R ═ RaObtaining the maximum distance deviation error caused by the intra-pulse motion of the frequency modulation continuous wave circular SAR to the whole observation scene, and comparing the maximum distance deviation error with the theoretical plane resolution delta rho 'at the center of the frequency modulation continuous wave circular SAR scene'0The division yields a ratio of the maximum range offset error due to intra-pulse motion to the resolution of Δ C, where Δ ρ'0＝2.4λ/(4πcosθd0)，
Figure GDA0002764024570000072
The pitch angle of the frequency modulation continuous wave circumference SAR to the scene center target is shown, wherein delta C is as follows:
Figure GDA0002764024570000073
step 4, judging whether the intra-pulse motion can be ignored in the imaging process of the frequency modulation continuous wave circular SAR time domain method and guiding to select a proper imaging method: substituting parameters of a frequency modulation continuous wave circular SAR imaging system into an expression of delta C and calculating the value of delta C, when the distance offset error caused by intra-pulse motion of the frequency modulation continuous wave circular SAR is smaller than a distance resolution unit, namely the delta C is smaller than 1, neglecting the distance offset error caused by intra-pulse motion in the imaging process by adopting a frequency modulation continuous wave circular SAR time domain method, neglecting the intra-pulse motion at the moment, and imaging by adopting a pulse system circular SAR time domain method, namely obtaining a final frequency modulation continuous wave circular SAR image by adopting a time domain imaging method of stop-go-stop approximation; on the contrary, when the distance offset error caused by the frequency modulation continuous wave circular SAR intra-pulse motion is more than or equal to one distance resolution unit, namely delta C is more than or equal to 1, intra-pulse motion cannot be ignored in the imaging process by adopting the frequency modulation continuous wave circular SAR time domain method, at the moment, extra compensation needs to be carried out on the intra-pulse motion, the imaging method for compensating the frequency modulation continuous wave circular SAR intra-pulse motion is adopted for imaging, and the following steps are continued;
step 5, imaging scene grid division, namely dividing the radar observation scene into a plurality of unit grids with consistent sizes, wherein the size requirement of the unit grids is smaller than the theoretical plane resolution delta rho at the scene center0', i.e. Δ x' < Δ ρ0′，Δy′＜Δρ0', where Δ x ' and Δ y ' are the range-wise spacing and azimuth-wise spacing of the scene mesh, respectively;
step 6, calculating a new instantaneous slope distance R' of the grid point at a certain azimuth slow moment and including a distance offset error introduced by intra-pulse platform motion, and the specific steps are as follows:
calculating the instantaneous slope distance R of the grid point under the approximate stop-go-stop at the azimuth momentcenComprises the following steps:
Figure GDA0002764024570000074
calculating the distance deviation error Delta R of the platform motion in the pulse introduced in the distance domain1Comprises the following steps:
Figure GDA0002764024570000075
wherein, Δ fi＝-2k1The/lambda is the frequency offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse in a distance domain, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a new instantaneous slope distance R ═ Rcen+ΔR1；
Step 7, calculating the corresponding position of the distance compression signal of the azimuth moment in the imaging grid according to the new instantaneous slant distance, namely projecting the distance compression signal of the azimuth moment into the imaging grid according to the new instantaneous slant distance and recording as Si′f(fi,tm)；
Step 8, azimuth phase compensation is carried out, and sub-images of a certain azimuth moment are obtained:
Figure GDA0002764024570000081
where x 'and y' are the grid coordinates in the scene, exp (j4 π R)Δm/λ) is an azimuth phase compensation function;
step 9, obtaining a final frequency modulation continuous wave circumferential SAR image, judging whether sub-images at all azimuth moments are obtained or not, namely whether sub-images at all sampling points in the azimuth direction are obtained or not, if not, entering the next azimuth moment and repeating the steps 6-8, and if sub-images at all azimuth moments are obtained, performing coherent superposition on the sub-images to obtain the final frequency modulation continuous wave circumferential SAR image:
Figure GDA0002764024570000082
wherein M is the number of sampling points in the azimuth direction in the whole 360-degree aperture.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all technical solutions that fall under the spirit of the present invention fall within the scope of the present invention. It should be noted that various modifications and adaptations to those skilled in the art without departing from the principles of the present invention should be considered as within the scope of the present invention.

Claims (1)

1. An imaging method for compensating circumferential SAR intra-pulse motion of frequency modulated continuous waves is characterized by comprising the following steps:
the method comprises the following steps of 1, acquiring frequency modulation continuous wave circular SAR echo signals, initializing parameters of a frequency modulation continuous wave circular SAR imaging system and modeling the frequency modulation continuous wave circular SAR echo signals, wherein the method is based on the following steps:
(1.1) initializing parameters of a frequency modulation continuous wave circular SAR imaging system: the radius of a circular motion track of the radar platform is R, the height is H, the azimuth observation angle is theta, and the phase center position A of the radar antenna is (x)r,yrH), wherein xr、yrAnd H are the x-axis, y-axis, and z-axis coordinates of position A, respectively, which may also be expressed as (R cos θ, R sin θ, H); the radius of the circular observation scene of the ground plane is RaThe coordinates of any point object P in the scene are (x, y,0), and can also be expressed as
Figure FDA0002764024560000011
Wherein r and
Figure FDA0002764024560000012
respectively the radial radius and azimuth angle of the target P; the radar motion angular speed is omega, the vehicle speed V is R omega, the azimuth observation angle corresponding to t time is theta t, and the full time
Figure FDA0002764024560000013
Wherein t ismWhich indicates a slow time in which the time,
Figure FDA0002764024560000014
the time is fast;
(1.2) modeling of a frequency modulation continuous wave circular SAR echo signal: instantaneous slope distance R between radar position A and target PrComprises the following steps:
Figure FDA0002764024560000015
calculation of RrAt a fast time
Figure FDA0002764024560000016
The first order taylor expansion of (a) is:
Figure FDA0002764024560000017
wherein the content of the first and second substances,
Figure FDA0002764024560000018
Figure FDA0002764024560000019
Rcenthe instantaneous slope distance under the stop-go-stop approximation, namely the instantaneous slope distance of the pulse system circumference SAR,
Figure FDA00027640245600000110
a range migration error introduced for the intra-pulse motion of the frequency-modulated continuous wave circular SAR is also an error ignored by the pulse circular SAR;
when the radar emission signal is a chirp signal, the echo signal of the target P is:
Figure FDA00027640245600000111
where rect (-) is a rectangular window function, c is the speed of light, TpIs pulse duration, and
Figure FDA00027640245600000112
fcis a carrier frequency, KrFrequency-modulated, and Kr＝B/TpB is the bandwidth of a radar emission signal;
step 2, the line-breaking frequency modulation processing, the residual video phase elimination and the fundamental frequency echo signal acquisition are carried out based on the following steps:
(2.1) line-breaking tone processing: echo signal
Figure FDA00027640245600000113
And a reference signal
Figure FDA00027640245600000114
The difference frequency signal obtained by the conjugate multiplication of (a) is:
Figure FDA00027640245600000115
wherein the reference signal
Figure FDA00027640245600000116
Comprises the following steps:
Figure FDA0002764024560000021
Rreffor reference distance, take the instantaneous slope distance, R, between the target at the center of the scene and the radarΔ＝Rr-Rref(ii) a Last exponential term in difference frequency signal
Figure FDA0002764024560000022
Is a residual video phase term;
(2.2) residual video phase elimination and fundamental frequency echo signal acquisition: the difference frequency signal is subjected to distance Fourier transform and is compared with an exponential term exp (-j pi f)i 2/Kr) Multiplying to eliminate residual video phase, where fi＝-2KrRΔThe/c is the difference frequency, and then the difference frequency is subjected to inverse Fourier transform to obtain a fundamental frequency echo signal:
Figure FDA0002764024560000023
wherein λ ═ fcC is the carrier wavelength, RΔm＝Rcen-Rref；
Step 3, compressing the distance and analyzing the distance deviation error caused by the platform motion in the vein, based on the following steps:
(3.1) distance compression: the phase corresponding to the last exponential term of the fundamental frequency echo signal is
Figure FDA0002764024560000024
Wherein
Figure FDA0002764024560000025
Has a coefficient of
Figure FDA0002764024560000026
The maximum value is 4 pi B/2c and is in the millimeter wave band fc> B/2, 4 pi/lambda-4 pi fc/c > 4 π B/2c, i.e. exponential terms in the fundamental echo signal
Figure FDA0002764024560000027
Corresponding phase is much smaller than
Figure FDA0002764024560000028
And (3) neglecting the influence of the last exponential term in the fundamental frequency signal on imaging, and then carrying out Fourier transform along the distance direction to obtain a distance compression signal as follows:
Figure FDA0002764024560000029
(3.2) analysisIntra-pulse motion induced distance offset error: the frequency offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse in the distance domain is delta fi＝-2k1λ, which is converted to a distance offset error of:
Figure FDA00027640245600000210
wherein, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a distance offset error Δ R1The maximum value of (a), namely the maximum distance offset error caused by the intra-pulse motion of the frequency-modulated continuous wave circular SAR to a certain target in the scene, is as follows:
Figure FDA00027640245600000211
in the above formula, let R ═ RaObtaining the maximum distance deviation error caused by the intra-pulse motion of the frequency modulation continuous wave circular SAR to the whole observation scene, and comparing the maximum distance deviation error with the theoretical plane resolution delta rho 'at the center of the frequency modulation continuous wave circular SAR scene'0The division yields a ratio of the maximum range offset error due to intra-pulse motion to the resolution of Δ C, where Δ ρ'0＝2.4λ/(4π cosθd0)，
Figure FDA00027640245600000212
The pitch angle of the frequency modulation continuous wave circumference SAR to the scene center target is shown, wherein delta C is as follows:
Figure FDA0002764024560000031
step 4, judging whether the intra-pulse motion can be ignored in the imaging process of the frequency modulation continuous wave circular SAR time domain method and guiding to select a proper imaging method: substituting parameters of a frequency modulation continuous wave circular SAR imaging system into an expression of delta C and calculating the value of delta C, when the distance offset error caused by intra-pulse motion of the frequency modulation continuous wave circular SAR is smaller than a distance resolution unit, namely the delta C is smaller than 1, neglecting the distance offset error caused by intra-pulse motion in the imaging process by adopting a frequency modulation continuous wave circular SAR time domain method, neglecting the intra-pulse motion at the moment, and imaging by adopting a pulse system circular SAR time domain method, namely obtaining a final frequency modulation continuous wave circular SAR image by adopting a time domain imaging method of stop-go-stop approximation; on the contrary, when the distance offset error caused by the frequency modulation continuous wave circular SAR intra-pulse motion is more than or equal to one distance resolution unit, namely delta C is more than or equal to 1, intra-pulse motion cannot be ignored in the imaging process by adopting the frequency modulation continuous wave circular SAR time domain method, at the moment, extra compensation needs to be carried out on the intra-pulse motion, the imaging method for compensating the frequency modulation continuous wave circular SAR intra-pulse motion is adopted for imaging, and the following steps are continued;
step 5, imaging scene grid division, namely dividing the radar observation scene into a plurality of unit grids with consistent sizes, wherein the size requirement of the unit grids is less than the theoretical plane resolution delta rho 'at the scene center'0I.e. Δ x '< Δ ρ'0，Δy′＜Δρ′0Wherein, Δ x 'and Δ y' are the distance interval and the azimuth interval of the scene grid, respectively;
step 6, calculating a new instantaneous slope distance R' of the grid point at a certain azimuth slow moment and including a distance offset error introduced by intra-pulse platform motion, and the specific steps are as follows:
calculating the instantaneous slope distance R of the grid point under the approximate stop-go-stop at the azimuth momentcenComprises the following steps:
Figure FDA0002764024560000032
calculating the distance deviation error Delta R of the platform motion in the pulse introduced in the distance domain1Comprises the following steps:
Figure FDA0002764024560000033
wherein, Δ fi＝-2k1The/lambda is the frequency offset error caused by the platform motion in the frequency modulation continuous wave circular SAR pulse in a distance domain, thetamIs a slow time tmCorresponding azimuthal observation angle, i.e. thetam＝ωtm；
Calculating a new instantaneous slope distance R ═ Rcen+ΔR1；
Step 7, calculating the corresponding position of the distance compressed signal at the azimuth moment in the imaging grid according to the new instantaneous slope distance, namely projecting the distance compressed signal at the azimuth moment into the imaging grid according to the new instantaneous slope distance and recording as S'if(fi,tm)；
Step 8, azimuth phase compensation is carried out, and sub-images of a certain azimuth moment are obtained:
Figure FDA0002764024560000034
where x 'and y' are the grid coordinates in the scene, exp (j4 π R)Δm/λ) is an azimuth phase compensation function;
step 9, obtaining a final frequency modulation continuous wave circumferential SAR image, judging whether sub-images at all azimuth moments are obtained or not, namely whether sub-images at all sampling points in the azimuth direction are obtained or not, if not, entering the next azimuth moment and repeating the steps 6-8, and if sub-images at all azimuth moments are obtained, performing coherent superposition on the sub-images to obtain the final frequency modulation continuous wave circumferential SAR image:
Figure FDA0002764024560000041
wherein M is the number of sampling points in the azimuth direction in the whole 360-degree aperture.
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