CN110221294A - Judgment method for neglecting platform motion in frequency modulation continuous wave circular SAR pulse - Google Patents

Judgment method for neglecting platform motion in frequency modulation continuous wave circular SAR pulse Download PDF

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CN110221294A
CN110221294A CN201910523301.5A CN201910523301A CN110221294A CN 110221294 A CN110221294 A CN 110221294A CN 201910523301 A CN201910523301 A CN 201910523301A CN 110221294 A CN110221294 A CN 110221294A
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frequency modulation
sar
arteries
circumference sar
signal
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CN110221294B (en
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • 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
    • G01S13/904—SAR modes
    • G01S13/9088—Circular SAR [CSAR, C-SAR]
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • 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
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9011—SAR image acquisition techniques with frequency domain processing of the SAR signals in azimuth

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  • Radar, Positioning & Navigation (AREA)
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  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Signal Processing (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention belongs to the technical field of radars, and discloses a judgment method for neglecting platform motion in frequency modulation continuous wave circular SAR veins, which comprises the following steps: (1) modeling a frequency modulation continuous wave circular SAR echo; (2) acquiring a time domain echo signal after the phase of the residual video of the frequency modulated continuous wave circular SAR is removed; (3) acquiring an echo signal of a frequency-modulated continuous wave circular SAR wave number domain; (4) acquiring a two-dimensional wave number spectrum of a frequency-modulated continuous wave circular SAR; (5) analyzing a phase error introduced by the platform motion in the pulse in a two-dimensional wave number domain; (6) and obtaining a judgment method for neglecting the motion of the platform in the pulse in the imaging process of the frequency modulation continuous wave circular SAR frequency domain method. The judgment method can quickly and efficiently judge whether the intra-pulse platform can be ignored in the imaging process of the system adopting a frequency domain method only by utilizing the parameters of the frequency modulation continuous wave circular SAR imaging system, and guides technicians to select a proper imaging method, so that theoretical support can be provided for simplifying the imaging process of the frequency modulation continuous wave circular SAR frequency domain method.

Description

A kind of decision method for ignoring the movement of CW with frequency modulation circumference SAR arteries and veins inner platform
Technical field
The invention belongs to Radar Technology fields, are related to synthetic aperture radar (Synthetic Aperture Radar, SAR) One of imaging technique frequency domain imaging method ignores the decision method of CW with frequency modulation circumference SAR arteries and veins inner platform movement.
Background technique
Infrared, photoelectronic reconnaissance equipment cannot work under adverse weather condition, using the limit by weather and environmental condition System.SAR is a kind of high-resolution imaging radar, can be under conditions of visibility is extremely low extremely severe complicated with environment to interested Target area carry out round-the-clock, round-the-clock reconnaissance and surveillance, and obtain similar photo-optical high-definition picture.But tradition Stripmap SAR is restricted since orientation accumulation angle is imaged in it, it is difficult to be obtained target scattering characteristics abundant, be limited azimuth discrimination The raising of rate, in many problems of high-resolution imaging field face, and its systematic comparison is complicated, at high cost, volume and weight Also larger, it is difficult to meet the application demand of miniaturization, low cost.Operating mode CW with frequency modulation circumference SAR new as one kind, The motion profile of its platform is circle, and transmitted waveform is CW with frequency modulation, irradiates the same circular field always during the motion Scape has subwavelength resolution, the advantages such as small in size, light weight and cost is low, carries earth observation application neck in Small and micro-satellite Domain has broad application prospects, and can answer for resource exploration, mapping, the condition of a disaster generaI investigation, urban planning and military surveillance etc. With offer high-definition picture.
For CW with frequency modulation circumference SAR due to the particularity of motion profile, traditional stripmap SAR imaging method is no longer suitable With and additional phase error can be introduced since radar platform continuously moves, the circumference SAR imaging method of pulse regime is not yet Again effectively.Time domain rear orientation projection (Back Projection, BP) method due to be suitable for arbitrary motion track SAR imaging and Precision is high, process is simple, is very suitable to circumference SAR imaging, but traditional time domain BP method is based on pulse regime, that is, uses Stop-walking-and stop approximation, is not suitable for pulse duration longer continuous wave system.Although can be by improving time domain BP method Make that it is suitable for CW with frequency modulation circumference SAR imagings, but there is a problem of that time domain approach imaging efficiency is low always.It is asked for this Topic, it is necessary to study the higher CW with frequency modulation circumference SAR frequency domain imaging method of imaging efficiency, almost there are no document reports at present The actual CW with frequency modulation circumference SAR frequency domain imaging method in road, and CW with frequency modulation circumference SAR actual for one is imaged System is used using that whether can ignore arteries and veins inner platform movement influence on RT in frequency domain method imaging process Stop-walking-and stop the circumference SAR frequency domain method under approximation to be imaged without quickly and effectively decision method, so that CW with frequency modulation circle All SAR frequency domain method imaging processes are more complex.
Summary of the invention
The object of the present invention is to for whether in CW with frequency modulation circumference SAR frequency domain method imaging process arteries and veins can be ignored Inner platform movement influence on RT and be imaged using stopping-walking-and stop the pulse regime circumference SAR frequency domain method under approximation The problem of, a kind of only related decision method with CW with frequency modulation circumference SAR imaging system parameters is provided, the decision method is available Whether can ignore the movement of arteries and veins inner platform in frequency domain method imaging process in quickly and effectively judging CW with frequency modulation circumference SAR It and guides technical staff to choose suitable imaging method, can be provided for the research of CW with frequency modulation circumference SAR frequency domain imaging method Theory support.
In order to achieve the above objectives, the present invention is achieved by the following technical solutions:
A kind of decision method for ignoring the movement of CW with frequency modulation circumference SAR arteries and veins inner platform, specifically includes the following steps:
Step 1 CW with frequency modulation circumference SAR echo modeling, including calculate CW with frequency modulation circumference SAR instantaneous oblique distance with And determine the echo-signal of CW with frequency modulation circumference SAR, it is based on following steps:
(1.1) calculate the instantaneous oblique distance of CW with frequency modulation circumference SAR: radar platform is in the plane that height is H with angle speed Degree ω moves in a circle, and circus movement orbital radius is R, and radar site is (Rcos θ, Rsin θ, H), and wherein θ is full-time t The azimuthal observation angle at moment, and θ=ω t,Wherein tmWithRespectively indicate slow time and fast time；Ground level scene In target position beWherein r is the radial radius of target,For the azimuth of target；Radar and mesh Instantaneous oblique distance R between markrAre as follows:
Further, by RrFirst order Taylor is carried out to be approximately:
Wherein,
RcenIt is that pulse regime circumference SAR stops-walking-and stops instantaneous oblique distance under approximation,It is CW with frequency modulation circumference SAR arteries and veins The additional range migration error that inner platform movement introduces；
(1.2) determine the echo-signal of CW with frequency modulation circumference SAR: the linear FM signal of radar emission indicates are as follows:
Wherein,TpFor pulse width, fcFor center frequency, KrFor frequency modulation rate；
The echo-signal of target is the delay time signal for emitting signal in the scene that radar receives, i.e., are as follows:
Wherein, c is the light velocity；
Step 2 obtains the time domain echo-signal after the removal of CW with frequency modulation circumference SAR Residual video phase, including frequency modulation removal The acquisition of time domain echo-signal after processing and Residual video phase removal, is based on following steps:
(2.1) deramp processing: by the distance between scene center and radar RrefAs reference distance, reference signalIt indicates are as follows:
Wherein, TrefFor the pulse persistance width of reference signal, it is slightly larger than Tp；
WithDeramp processing can be realized in multiplication, whereinIndicate reference signalConjugation, obtain intermediate-freuqncy signal are as follows:
Wherein, RΔ=Rr-Rref,For Residual video phase item；
(2.2) acquisition of time domain echo-signal after Residual video phase removes: needed for Residual video phase is eliminated and obtained Time domain echo-signalProcedural representation are as follows:
Wherein,WithRespectively indicate Fourier transformation and inverse Fourier transform, fi=-2KrRΔ/ c is intermediate frequency Frequency, λ=fc/ c is carrier wavelength, RΔm=Rcen-Rref；
Step 3 obtains CW with frequency modulation circumference SAR wave-number domain echo-signal, defines distance to wave numberCarry it into time domain echo-signalIn, obtain CW with frequency modulation circumference SAR wave-number domain Echo-signal are as follows:
Wherein, B is radar emission signal bandwidth, fast timeK can be usedRIt indicates, i.e. Sr(KR,tm) it is only distance to wave number KRWith slow time tmFunction；
Step 4 obtains the two-dimentional wave-number spectrum of CW with frequency modulation circumference SAR, the spectral theory expression including determining two-dimentional wave number Formula calculates point in phase bit and determines the approximate expression of two-dimentional wave-number spectrum, is based on following steps:
(4.1) theoretical expression of two-dimentional wave-number spectrum is determined: by wave-number domain echo-signal Sr(KR,tm) along azimuthal observation angle θmFourier transformation is done, wherein θm=ω tmFor tmMoment corresponding azimuthal observation angle, and ignore rectangular window function and constant phase Item exp (jKRRref), obtain the theoretical expression of CW with frequency modulation circumference SAR two dimension wave-number spectrum are as follows:
Wherein, ξ is that orientation angles tie up wave number；
(4.2) it calculates point in phase bit: calculating the approximate expression of two-dimentional wave-number spectrum using principle in phase bit to above formula Formula, in the calculating process of point in phase bit, due toIgnore exponential termTo point in phase bit It influences, therefore, the equation for solving point in phase bit becomes:
Wherein, a2=R2+r2+H2, b=Rr；
It solves above formula and obtains two points in phase bitWithAnd there is following relationship:
(4.3) approximate expression of two-dimentional wave-number spectrum is determined: willWithBring two dimension into respectively The theoretical expression of wave-number spectrum obtains two sub- frequency spectrum SI(KR, ξ) and SII(KR, ξ), then the two-dimentional wave of CW with frequency modulation circumference SAR Number spectrum is made of the two sub- spectral overlays, approximate expression are as follows:
S(KR, ξ) and=SI(KR,ξ)+SII(KR,ξ)
Wherein,
Wherein, V=R ω is radar motion speed, | | expression takes absolute value；
Step 5 analysis arteries and veins inner platform moves the phase error introduced in two-dimentional wave-number domain, CW with frequency modulation circumference SAR two The last one exponential term in sub- frequency spectrumIt is that the movement of arteries and veins inner platform introduces, in pulse circumference SAR, by Stop-walking-in using and stop approximation, which is ignored, and in CW with frequency modulation circumference SAR, which contains arteries and veins The information of inner platform movement is converted into arteries and veins inner platform and moves the phase error introduced in two-dimentional wave-number domain are as follows:
The maximum value for calculating above formula obtains the movement of CW with frequency modulation circumference SAR arteries and veins inner platform and exists to target a certain in scene Maximum phase error caused by two-dimentional wave-number domain are as follows:
R=R is enabled in above formulaa, wherein RaFor the radius of circle observation scene, CW with frequency modulation circumference SAR arteries and veins inner platform is obtained Movement caused maximum phase error in entirely observation scene are as follows:
Step 6 obtains the judgement side for ignoring the movement of arteries and veins inner platform in CW with frequency modulation circumference SAR frequency domain method imaging process Method enables Δ P=Pemax_w/ (π/4), then Δ P is indicated are as follows:
It brings in the expression formula of Δ P and calculates CW with frequency modulation circumference SAR imaging system parameters the value of Δ P into, work as frequency modulation When maximum phase error caused by continuous wave circumference SAR arteries and veins inner platform moves is less than π/4, i.e. Δ P < 1, using CW with frequency modulation The movement of circumference SAR frequency domain method imaging process middle arteries inner platform causes phase error can be ignored, and can ignore arteries and veins at this time Inner platform movement；Conversely, when CW with frequency modulation circumference SAR arteries and veins inner platform move caused by maximum phase error be greater than or equal to π/ When 4, i.e. Δ P >=1, using the movement of arteries and veins inner platform cannot be ignored in CW with frequency modulation circumference SAR frequency domain method imaging process, at this time It needs to move the phase error introduced to arteries and veins inner platform and carries out additional compensation.
A kind of decision method for ignoring the movement of CW with frequency modulation circumference SAR arteries and veins inner platform of the present invention, the beneficial effect is that:
By establishing CW with frequency modulation circumference SAR wave-number domain signal model and 2-d spectrum, CW with frequency modulation circle has been obtained All SAR arteries and veins inner platform movements can introduce additional phase error in two-dimentional wave-number domain, analyze the phase error and obtained frequency modulation company Ignore the decision method of arteries and veins inner platform movement in continuous wave circumference SAR frequency domain method imaging process, the decision method is merely with frequency modulation Continuous wave circumference SAR imaging system parameters can rapidly and efficiently judgement one actual CW with frequency modulation circumference SAR imaging system Whether system can ignore the movement of arteries and veins inner platform in using CW with frequency modulation circumference SAR frequency domain method imaging process, and then instruct Suitable frequency domain imaging method is chosen, theory support can be provided for the research of CW with frequency modulation circumference SAR frequency domain imaging method.
Detailed description of the invention
Fig. 1 is the general frame that the present invention ignores that CW with frequency modulation circumference SAR arteries and veins inner platform moves decision method.
Specific embodiment
Technical solution in order to better illustrate the present invention is with reference to the accompanying drawing made embodiments of the present invention further Ground description.
Fig. 1 is the general frame ignored CW with frequency modulation circumference SAR arteries and veins inner platform and move decision method of the invention, specifically Include the following steps:
Step 1 CW with frequency modulation circumference SAR echo modeling, including calculate CW with frequency modulation circumference SAR instantaneous oblique distance with And determine the echo-signal of CW with frequency modulation circumference SAR, it is based on following steps:
(1.1) calculate the instantaneous oblique distance of CW with frequency modulation circumference SAR: radar platform is in the plane that height is H with angle speed Degree ω moves in a circle, and circus movement orbital radius is R, and radar site is (Rcos θ, Rsin θ, H), and wherein θ is full-time t The azimuthal observation angle at moment, and θ=ω t,Wherein tmWithRespectively indicate slow time and fast time；Ground level scene In target position beWherein r is the radial radius of target,For the azimuth of target；Radar and mesh Instantaneous oblique distance R between markrAre as follows:
Further, by RrFirst order Taylor is carried out to be approximately:
Wherein,
RcenIt is that pulse regime circumference SAR stops-walking-and stops instantaneous oblique distance under approximation,It is CW with frequency modulation circumference SAR arteries and veins The additional range migration error that inner platform movement introduces；
(1.2) determine the echo-signal of CW with frequency modulation circumference SAR: the linear FM signal of radar emission indicates are as follows:
Wherein,TpFor pulse width, fcFor center frequency, KrFor frequency modulation rate；
The echo-signal of target is the delay time signal for emitting signal in the scene that radar receives, i.e., are as follows:
Wherein, c is the light velocity；
Step 2 obtains the time domain echo-signal after the removal of CW with frequency modulation circumference SAR Residual video phase, including frequency modulation removal The acquisition of time domain echo-signal after processing and Residual video phase removal, is based on following steps:
(2.1) deramp processing: by the distance between scene center and radar RrefAs reference distance, reference signalIt indicates are as follows:
Wherein, TrefFor the pulse persistance width of reference signal, it is slightly larger than Tp；
WithDeramp processing can be realized in multiplication, whereinIndicate reference signalConjugation, obtain intermediate-freuqncy signal are as follows:
Wherein, RΔ=Rr-Rref,For Residual video phase item；
(2.2) acquisition of time domain echo-signal after Residual video phase removes: needed for Residual video phase is eliminated and obtained Time domain echo-signalProcedural representation are as follows:
Wherein,WithRespectively indicate Fourier transformation and inverse Fourier transform, fi=-2KrRΔ/ c is intermediate frequency Frequency, λ=fc/ c is carrier wavelength, RΔm=Rcen-Rref；
Step 3 obtains CW with frequency modulation circumference SAR wave-number domain echo-signal, defines distance to wave numberCarry it into time domain echo-signalIn, obtain CW with frequency modulation circumference SAR wave-number domain Echo-signal are as follows:
Wherein, B is radar emission signal bandwidth；
Step 4 obtains the two-dimentional wave-number spectrum of CW with frequency modulation circumference SAR, the theoretical expression including determining two-dimentional wave-number spectrum Formula calculates point in phase bit and determines the approximate expression of two-dimentional wave-number spectrum, is based on following steps:
(4.1) theoretical expression of two-dimentional wave-number spectrum is determined: by wave-number domain echo-signal Sr(KR,tm) along azimuthal observation angle θmFourier transformation is done, wherein θm=ω tmFor tmMoment corresponding azimuthal observation angle, and ignore rectangular window function and constant phase Item exp (jKRRref), obtain the theoretical expression of CW with frequency modulation circumference SAR two dimension wave-number spectrum are as follows:
Wherein, ξ is that orientation angles tie up wave number；
(4.2) it calculates point in phase bit: calculating the approximate expression of two-dimentional wave-number spectrum using principle in phase bit to above formula Formula, in the calculating process of point in phase bit, due toIgnore exponential termTo point in phase bit It influences, therefore, the equation for solving point in phase bit becomes:
Wherein, a2=R2+r2+H2, b=Rr；
It solves above formula and obtains two points in phase bitWithAnd there is following relationship:
(4.3) approximate expression of two-dimentional wave-number spectrum is determined: willWithBring two dimension into respectively The theoretical expression of wave-number spectrum obtains two sub- frequency spectrum SI(KR, ξ) and SII(KR, ξ), then the two-dimentional wave of CW with frequency modulation circumference SAR Number spectrum is made of the two sub- spectral overlays, approximate expression are as follows:
S(KR, ξ) and=SI(KR,ξ)+SII(KR,ξ)
Wherein,
Wherein, V=R ω is radar motion speed, | | expression takes absolute value；
Step 5 analysis arteries and veins inner platform moves the phase error introduced in two-dimentional wave-number domain, CW with frequency modulation circumference SAR two The last one exponential term in sub- frequency spectrumIt is that the movement of arteries and veins inner platform introduces, in pulse circumference SAR, by Stop-walking-in using and stop approximation, which is ignored, and in CW with frequency modulation circumference SAR, which contains arteries and veins The information of inner platform movement is converted into arteries and veins inner platform and moves the phase error introduced in two-dimentional wave-number domain are as follows:
The maximum value for calculating above formula obtains the movement of CW with frequency modulation circumference SAR arteries and veins inner platform and exists to target a certain in scene Maximum phase error caused by two-dimentional wave-number domain are as follows:
R=R is enabled in above formulaa, wherein RaFor the radius of circle observation scene, CW with frequency modulation circumference SAR arteries and veins inner platform is obtained Movement caused maximum phase error in entirely observation scene are as follows:
Step 6 obtains the judgement side for ignoring the movement of arteries and veins inner platform in CW with frequency modulation circumference SAR frequency domain method imaging process Method enables Δ P=Pemax_w/ (π/4), then Δ P is indicated are as follows:
It brings in the expression formula of Δ P and calculates CW with frequency modulation circumference SAR imaging system parameters the value of Δ P into, work as frequency modulation When maximum phase error caused by continuous wave circumference SAR arteries and veins inner platform moves is less than π/4, i.e. Δ P < 1, using CW with frequency modulation The movement of circumference SAR frequency domain method imaging process middle arteries inner platform causes phase error can be ignored, and can ignore arteries and veins at this time Inner platform movement；Conversely, when CW with frequency modulation circumference SAR arteries and veins inner platform move caused by maximum phase error be greater than or equal to π/ When 4, i.e. Δ P >=1, using the movement of arteries and veins inner platform cannot be ignored in CW with frequency modulation circumference SAR frequency domain method imaging process, at this time It needs to move the phase error introduced to arteries and veins inner platform and carries out additional compensation.
The above is only presently preferred embodiments of the present invention, is not intended to limit the scope of the present invention, all categories Technical solution under thinking of the present invention all belongs to the scope of protection of the present invention.It should be pointed out that for the common of the art For technical staff, several improvements and modifications without departing from the principles of the present invention should be considered as falling into guarantor of the invention Protect range.

Claims (1)

1. a kind of decision method for ignoring the movement of CW with frequency modulation circumference SAR arteries and veins inner platform, which is characterized in that under this method includes Column step:
Step 1 CW with frequency modulation circumference SAR echo modeling, including calculate CW with frequency modulation circumference SAR instantaneous oblique distance and really Determine the echo-signal of CW with frequency modulation circumference SAR, be based on following steps:
(1.1) calculate the instantaneous oblique distance of CW with frequency modulation circumference SAR: radar platform is in the plane that height is H with angular velocity omega It moves in a circle, circus movement orbital radius is R, and radar site is (Rcos θ, Rsin θ, H), and wherein θ is full-time t moment Azimuthal observation angle, and θ=ω t,Wherein tmWithRespectively indicate slow time and fast time；In ground level scene Target position isWherein r is the radial radius of target,For the azimuth of target；Radar and target it Between instantaneous oblique distance RrAre as follows:
Further, by RrFirst order Taylor is carried out to be approximately:
Wherein,
RcenIt is that pulse regime circumference SAR stops-walking-and stops instantaneous oblique distance under approximation,It is to be put down in CW with frequency modulation circumference SAR arteries and veins The additional range migration error that platform movement introduces；
(1.2) determine the echo-signal of CW with frequency modulation circumference SAR: the linear FM signal of radar emission indicates are as follows:
Wherein,TpFor pulse width, fcFor center frequency, KrFor frequency modulation rate；
The echo-signal of target is the delay time signal for emitting signal in the scene that radar receives, i.e., are as follows:
Wherein, c is the light velocity；
Step 2 obtains the time domain echo-signal after the removal of CW with frequency modulation circumference SAR Residual video phase, including deramp processing And Residual video phase removal after time domain echo-signal acquisition, be based on following steps:
(2.1) deramp processing: by the distance between scene center and radar RrefAs reference distance, reference signal It indicates are as follows:
Wherein, TrefFor the pulse persistance width of reference signal, it is slightly larger than Tp；
WithDeramp processing can be realized in multiplication, whereinIndicate reference signal Conjugation, obtain intermediate-freuqncy signal are as follows:
Wherein, RΔ=Rr-Rref,For Residual video phase item；
(2.2) after Residual video phase removal time domain echo-signal acquisition: when Residual video phase is eliminated and obtains required Domain echo-signalProcedural representation are as follows:
Wherein,WithRespectively indicate Fourier transformation and inverse Fourier transform, fi=-2KrRΔ/ c is IF frequency, λ =fc/ c is carrier wavelength, RΔm=Rcen-Rref；
Step 3 obtains CW with frequency modulation circumference SAR wave-number domain echo-signal, defines distance to wave numberCarry it into time domain echo-signalIn, obtain CW with frequency modulation circumference SAR wave-number domain Echo-signal are as follows:
Wherein, B is radar emission signal bandwidth, fast timeK can be usedRIt indicates, i.e. Sr(KR,tm) it is only distance to wave number KRWith Slow time tmFunction；
Step 4 obtains the two-dimentional wave-number spectrum of CW with frequency modulation circumference SAR, the spectral theory expression formula including determining two-dimentional wave number, meter It calculates point in phase bit and determines the approximate expression of two-dimentional wave-number spectrum, be based on following steps:
(4.1) theoretical expression of two-dimentional wave-number spectrum is determined: by wave-number domain echo-signal Sr(KR,tm) along azimuthal observation angle θmIt is Fu In leaf transformation, wherein θm=ω tmFor tmMoment corresponding azimuthal observation angle, and ignore rectangular window function and constant phase item exp (jKRRref), obtain the theoretical expression of CW with frequency modulation circumference SAR two dimension wave-number spectrum are as follows:
Wherein, ξ is that orientation angles tie up wave number；
(4.2) it calculates point in phase bit: calculating the approximate expression of two-dimentional wave-number spectrum using principle in phase bit to above formula, In the calculating process of point in phase bit, due toIgnore exponential termInfluence to point in phase bit, Therefore, the equation for solving point in phase bit becomes:
Wherein, a2=R2+r2+H2, b=Rr；
It solves above formula and obtains two points in phase bitWithAnd there is following relationship:
(4.3) approximate expression of two-dimentional wave-number spectrum is determined: willWithBring two-dimentional wave number into respectively The theoretical expression of spectrum obtains two sub- frequency spectrum SI(KR, ξ) and SII(KR, ξ), then the two-dimentional wave-number spectrum of CW with frequency modulation circumference SAR It is made of the two sub- spectral overlays, approximate expression are as follows:
S(KR, ξ) and=SI(KR,ξ)+SII(KR,ξ)
Wherein,
Wherein, V=R ω is radar motion speed, | | expression takes absolute value；
Step 5 analysis arteries and veins inner platform moves the phase error introduced in two-dimentional wave-number domain, two son frequencies of CW with frequency modulation circumference SAR The last one exponential term in spectrumIt is that the movement of arteries and veins inner platform introduces, in pulse circumference SAR, due to adopting Stop approximation with-walking-is stopped, which is ignored, and in CW with frequency modulation circumference SAR, which contains in arteries and veins and puts down The information of platform movement is converted into arteries and veins inner platform and moves the phase error introduced in two-dimentional wave-number domain are as follows:
The maximum value for calculating above formula obtains the movement of CW with frequency modulation circumference SAR arteries and veins inner platform to target a certain in scene in two dimension Maximum phase error caused by wave-number domain are as follows:
R=R is enabled in above formulaa, wherein RaFor the radius of circle observation scene, the movement of CW with frequency modulation circumference SAR arteries and veins inner platform is obtained The caused maximum phase error in entirely observation scene are as follows:
Step 6 obtains the decision method for ignoring the movement of arteries and veins inner platform in CW with frequency modulation circumference SAR frequency domain method imaging process, enables Δ P=Pemax_w/ (π/4), then Δ P is indicated are as follows:
CW with frequency modulation circumference SAR imaging system parameters are brought in the expression formula of Δ P and calculate the value of Δ P into, when frequency modulation is continuous When maximum phase error caused by wave circumference SAR arteries and veins inner platform moves is less than π/4, i.e. Δ P < 1, using CW with frequency modulation circumference The movement of SAR frequency domain method imaging process middle arteries inner platform causes phase error can be ignored, and can ignore in arteries and veins at this time and put down Platform movement；Conversely, the maximum phase error caused by CW with frequency modulation circumference SAR arteries and veins inner platform moves is greater than or equal to π/4, i.e., When Δ P >=1, using the movement of arteries and veins inner platform cannot be ignored in CW with frequency modulation circumference SAR frequency domain method imaging process, need at this time The phase error introduced to the movement of arteries and veins inner platform carries out additional compensation.
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