CN108594229A - The compensation method of Doppler effect two dimension, device and storage medium in satellite-borne SAR arteries and veins - Google Patents

The compensation method of Doppler effect two dimension, device and storage medium in satellite-borne SAR arteries and veins Download PDF

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CN108594229A
CN108594229A CN201810399422.9A CN201810399422A CN108594229A CN 108594229 A CN108594229 A CN 108594229A CN 201810399422 A CN201810399422 A CN 201810399422A CN 108594229 A CN108594229 A CN 108594229A
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dimensional
azimuth
satellite
distance
doppler
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CN108594229B (en
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王伟
王宇
邓云凯
禹卫东
张志敏
齐向阳
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Institute of Electronics of CAS
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004SAR image acquisition techniques
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904SAR modes
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses the compensation method of Doppler effect two dimension, device and computer readable storage medium in a kind of satellite-borne SAR arteries and veins, the method includes:Based on using the orientation time as the Doppler frequency shift amount of variable, satellite-borne SAR two dimension echo model is obtained;To the satellite-borne SAR two dimension echo model respectively into row distance to Fourier transformation and orientation Fourier transformation, distance is obtained to the two-dimensional frequency echo model with orientation;Doppler frequency shift item based on from the distance to the two-dimensional frequency echo model with orientation, obtains Doppler shift compensation function.

Description

Satellite-borne SAR intra-pulse Doppler effect two-dimensional compensation method and device and storage medium
Technical Field
The present invention relates to a satellite-borne Synthetic Aperture Radar (SAR) intra-pulse doppler effect compensation technique, and in particular, to a satellite-borne SAR intra-pulse doppler effect two-dimensional compensation method, device, and storage medium.
Background
According to SAR imaging theory, the azimuthal signal originates from relative motion between the radar and the target, which typically introduces doppler frequency shifts. At present, the platform speed of the satellite-borne SAR is high, so the Doppler bandwidth is high generally, and the satellite-borne SAR also has high Doppler center frequency when an oblique angle exists. This introduces a high intra-pulse doppler shift. Different radar transmission waveforms have different doppler tolerance, and in the case of a non-chirped signal, the doppler shift tolerance is poor. And the echo frequency shift amount of the same point target is time-varying along the azimuth direction along with the change of the relative positions of the radar and the point target. This can defocus the point target, degrading SAR imaging performance.
In summary, how to compensate the intra-pulse doppler effect under the satellite-borne condition is a problem to be solved urgently.
Disclosure of Invention
In view of the above, the main objective of the present invention is to provide a two-dimensional compensation method, device and storage medium for intra-pulse doppler effect of a satellite-borne SAR, which can effectively compensate the intra-pulse doppler effect of a satellite-borne SAR echo.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the embodiment of the invention provides a two-dimensional compensation method for an intra-pulse Doppler effect of a satellite-borne SAR, which comprises the following steps:
obtaining a satellite-borne SAR two-dimensional echo model based on a Doppler frequency shift quantity with azimuth time as a variable;
respectively carrying out distance direction Fourier transform and azimuth direction Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance direction and azimuth direction two-dimensional frequency domain echo model;
obtaining a Doppler frequency shift compensation function based on a Doppler frequency shift term in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction;
and acquiring echo data, and performing range pulse compression on the echo data based on the Doppler frequency shift compensation function.
Wherein, the satellite-borne SAR two-dimensional echo model is as follows:
wherein the first phase termIs a frequency shift portion; a. the0is a constant, t is the distance direction fast time, η is the azimuth direction slow time, ηcfor the beam center time, c is the propagation velocity of the transmit signal, λ is the wavelength of the transmit signal, φ (-) is the time domain phase of the transmit signal, R (η) is the target slope distance varying along the azimuth time, R' (η) is the first derivative of R (η), wr(. is a distance-to-time envelope, wa(. cndot.) is the azimuth time envelope.
The two-dimensional frequency domain echo model of the distance direction and the azimuth direction is as follows:
wherein f isηIs the azimuth frequency, Wa(fη) Is the azimuthal spectral envelope. Thetaa(ft,fη) Comprises the following steps:
wherein, VSIs the speed of the platform of the spaceborne SAR.
Wherein the Doppler shift compensation function is:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*
wherein FTt(. cndot.) is a distance-to-Fourier transform.
The embodiment of the invention provides a two-dimensional compensation device for an intra-pulse Doppler effect of a satellite-borne SAR, which comprises:
the echo model building unit is used for obtaining a satellite-borne SAR two-dimensional echo model based on the Doppler frequency shift quantity taking azimuth time as a variable;
the Fourier transform unit is used for respectively carrying out distance Fourier transform and azimuth Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance-direction and azimuth-direction two-dimensional frequency domain echo model;
the compensation function building unit is used for obtaining a Doppler frequency shift compensation function based on Doppler frequency shift terms in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction;
an acquisition unit for acquiring echo data;
and the range pulse compression unit is used for performing range pulse compression on the echo data based on the Doppler frequency shift compensation function.
Wherein, the satellite-borne SAR two-dimensional echo model is as follows:
wherein the first phase termIs a frequency shift portion; a. the0is a constant, t is the distance direction fast time, η is the azimuth direction slow time, ηcfor the beam center time, c is the propagation velocity of the transmit signal, λ is the wavelength of the transmit signal, φ (-) is the time domain phase of the transmit signal, R (η) is the target slope distance varying along the azimuth time, R' (η) is the first derivative of R (η), wr(. is a distance-to-time envelope, wa(. cndot.) is the azimuth time envelope.
The two-dimensional frequency domain echo model of the distance direction and the azimuth direction is as follows:
wherein f isηIs the azimuth frequency, Wa(fη) Is the azimuthal spectral envelope. Thetaa(ft,fη) Comprises the following steps:
wherein, VSIs the speed of the platform of the spaceborne SAR.
Wherein the Doppler shift compensation function is:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*
wherein FTt(. cndot.) is a distance-to-Fourier transform.
An embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the two-dimensional compensation method for the intra-pulse doppler effect of the satellite-borne SAR.
In the technical scheme of the embodiment of the scheme, the two-dimensional compensation method for the satellite-borne SAR intra-pulse Doppler effect comprises the following steps: obtaining a satellite-borne SAR two-dimensional echo model based on a Doppler frequency shift quantity with azimuth time as a variable; respectively carrying out distance direction Fourier transform and azimuth direction Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance direction and azimuth direction two-dimensional frequency domain echo model; obtaining a Doppler frequency shift compensation function based on a Doppler frequency shift term in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction; and acquiring echo data, and performing range pulse compression on the echo data based on the Doppler frequency shift compensation function. Therefore, the compensation of the Doppler effect in the real pulse under the satellite-borne condition is realized, and the obtained compensation result can be further utilized by the traditional imaging algorithm, so that the accurate focusing of the image is completed.
Drawings
Fig. 1 is a schematic flow chart of a two-dimensional compensation method for an intra-pulse doppler effect of a satellite-borne SAR according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a focusing result of a point target under an oblique viewing condition according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a point target focusing result after Doppler effect compensation according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a two-dimensional compensation device for the intra-pulse doppler effect of a satellite-borne SAR according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Fig. 1 is a schematic flow chart of a two-dimensional compensation method for an intra-pulse doppler effect of a satellite-borne SAR according to an embodiment of the present invention, as shown in fig. 1, the method includes the following steps:
step 101: obtaining a satellite-borne SAR two-dimensional echo model based on a Doppler frequency shift quantity with azimuth time as a variable;
specifically, SAR is two-dimensional imaging, and the amount of doppler shift of the echo of the same point target in a synthetic aperture time is changed with azimuth time, so that the doppler shift changing with azimuth time must be introduced into the SAR two-dimensional echo. After adding the Doppler frequency shift, the SAR echo expression based on the point target is as follows:
wherein the first phase termRepresenting a frequency-shifted portion; a. the0is constant, t represents the fast time of the distance direction, η denotes the slow time of the azimuth direction, etacrepresenting the time of the beam centre, c the propagation velocity of the transmitted signal, λ the wavelength of the transmitted signal, (. phi.) the time domain phase of the transmitted signal, R (η) the target slope distance varying with time along the azimuth, R' (η) the first derivative of R (η), wr() represents a distance-to-time envelope; w is aa(-) represents the azimuth time envelope.
Wherein A is0According to the specific detection environment (such as the material of the point target).
Step 102: respectively carrying out distance direction Fourier transform and azimuth direction Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance direction and azimuth direction two-dimensional frequency domain echo model;
specifically, based on the two-dimensional SAR echo model containing the Doppler frequency shift term given by the formula (1), a two-dimensional frequency domain echo model independent of the signal form is derived. Firstly, distance Fourier transform is carried out on a two-dimensional echo model containing Doppler effect based on a stationary phase principle to obtain:
wherein f istRepresents a range frequency; wr(ft) Representing a distance-wise spectral envelope; f. ofcRepresenting the center frequency of the carrier frequency of the transmitted signal. Since the analytic expression of the frequency domain phase of the signal is sometimes difficult to obtain, it is uniformly used Θ (f) heret) And (4) showing. And (3) continuing to perform azimuth Fourier transform on the formula, wherein the two-dimensional frequency domain echo model can be approximately expressed as:
wherein f isηRepresenting the azimuth frequency; wa(fη) Representing an azimuthal spectral envelope; thetaa(ft,fη) The following can be written:
wherein, VSIs the speed of the platform of the spaceborne SAR.
The two-dimensional frequency domain echo model of the distance direction and the azimuth direction is obtained by performing distance direction fourier transform and then azimuth direction fourier transform on the satellite-borne SAR two-dimensional echo model, and in actual processing, the two-dimensional frequency domain echo model of the satellite-borne SAR may also be performed by performing azimuth direction fourier transform and then distance direction fourier transform, which is not described herein again.
Step 103: and obtaining a Doppler frequency shift compensation function based on the Doppler frequency shift term in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction.
The doppler shift term is expressed in the first phase term of equation (3), and the embodiment of the present invention constructs a doppler shift compensation function of the following form:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*(5)
wherein FTt(. cndot.) represents a distance-to-fourier transform. Equation (5) is used to multiply equation (3) in the frequency domain to compensate for the first phase term of equation (3).
Step 104: and acquiring echo data, and performing range pulse compression on the echo data based on the Doppler frequency shift compensation function.
The echo is received through the antenna, the echo data needing to be compensated is obtained, the obtained echo data is multiplied by the formula (5) in a frequency domain based on the formula (5), the frequency shift item of the echo data is compensated, and after the first phase item is compensated, the distance pulse compression of the signal is completed, so that the compensation result of the invention is obtained. And then, according to the compensation result, the traditional imaging algorithm is utilized to finish focusing imaging on the signal.
In the embodiment of the invention, the influence of Doppler frequency shift on two-dimensional time domain echo and a general echo description model independent of a signal form are provided, the compensation of Doppler effect in real pulse under a satellite-borne condition is realized, and the accurate focusing of an image is completed.
The function of the present invention will be described in further detail with reference to specific examples.
Generally, because the platform speed of the space-borne SAR is much higher than that of the airborne SAR, the doppler shift thereof is also usually much higher than that of the airborne SAR. For example: the satellite-borne SAR with the platform effective speed of 7100m/s has the Doppler frequency range of-2189.3 Hz to 2189.3Hz under the condition that the squint angle is zero when the beam width is 1 degree (deg). And for an airborne SAR with a speed of 150m/s, the doppler frequency range is-46.3 Hz to 46.3 Hz. The performance of the radar signal decreases gradually as the doppler shift increases. The doppler shift has a more severe impact on the on-board SAR imaging under squint conditions. The effect was analyzed by simulation as follows:
the simulation parameters are shown in table 1:
system parameter
TABLE 1
Taking the nonlinear frequency modulation signal as an example, the nonlinear frequency modulation signal with the matched filtering output-45 dB sidelobe is constructed to be used as a radar emission waveform. Let the radar squint angle be thetacThen its Doppler center frequency isηcRepresenting the beam center time instant. For example, when the squint angle is 10deg, the doppler center frequency is 43565Hz, so the absolute value of the doppler shift is further increased under the squint condition. The result of the point target echo obtained through simulation and imaging is shown in fig. 2, and it can be seen from fig. 2 that the point target is not well focused under the oblique condition, and the imaging is distorted.
The result of performing frequency shift compensation and focusing imaging on the doppler effect compensation method of the embodiment of the invention is shown in fig. 3. Comparing fig. 2 and fig. 3, it can be known that the point target echo signal is well focused after doppler shift compensation is performed on the signal in the two-dimensional frequency domain. The simulation result verifies the effectiveness of the method.
Fig. 4 is a schematic structural diagram of a two-dimensional satellite-borne SAR intra-pulse doppler effect compensation device according to an embodiment of the present invention, as shown in fig. 4, the device includes: echo model construction section 401, fourier transform section 402, compensation function construction section 403, acquisition section 404, and range direction pulse compression section 405. Wherein,
the echo model constructing unit 401 is configured to obtain a satellite-borne SAR two-dimensional echo model based on a doppler frequency shift amount using azimuth time as a variable;
a fourier transform unit 402, configured to perform distance-to-fourier transform and azimuth-to-fourier transform on the satellite-borne SAR two-dimensional echo model respectively to obtain distance-to-azimuth two-dimensional frequency domain echo models;
a compensation function constructing unit 403, configured to obtain a doppler shift compensation function based on a doppler shift term in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction;
an obtaining unit 404, configured to obtain echo data;
a range direction pulse compression unit 405, configured to perform range direction pulse compression on the echo data based on the doppler shift compensation function.
In this embodiment, the two-dimensional echo model of the satellite-borne SAR obtained by the echo model building unit 401 is:
wherein the first phase termIs a frequency shift portion; a. the0is a constant, t is the distance direction fast time, η is the azimuth direction slow time, ηcfor the beam center time, c is the electromagnetic wave propagation velocity, λ is the wavelength, φ (-) is the time domain phase of the transmitted signal, R (η) is the target slope distance along the azimuth time variation, R' (η) is the first derivative of R (η), wr(. is a distance-to-time envelope, wa(. cndot.) is the azimuth time envelope.
In this embodiment, the two-dimensional frequency domain echo model of the distance direction and the azimuth direction obtained by the fourier transform unit 402 is:
wherein f isηIs the azimuth frequency, Wa(fη) Is the azimuthal spectral envelope. Thetaa(ft,fη) Comprises the following steps:
in this embodiment, the doppler shift compensation function obtained by the compensation function constructing unit 403 is:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*
wherein FTt(. cndot.) is a distance-to-Fourier transform.
In the embodiment of the invention, a general echo description model independent of a signal form is obtained based on the echo model constructing unit 401 and the Fourier transform unit 402, and compensation of the Doppler effect in real pulses under a satellite-borne condition is realized based on the compensation function constructing unit 403 and the range direction pulse compression unit 405, so that accurate focusing of an image is completed.
It should be understood by those skilled in the art that the implementation functions of each unit in the two-dimensional compensation device for the satellite-borne SAR intra-pulse doppler effect shown in fig. 4 can be understood by referring to the related description of the aforementioned two-dimensional compensation method for the satellite-borne SAR intra-pulse doppler effect. The functions of the units in the two-dimensional compensation device for the intra-pulse doppler effect of the satellite-borne SAR shown in fig. 4 can be realized by a program running on a processor, and can also be realized by a specific logic circuit.
The embodiment of the present invention further describes a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the two-dimensional compensation method for the intra-pulse doppler effect of the satellite-borne SAR of the foregoing embodiment.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (9)

1. A two-dimensional compensation method for an intra-pulse Doppler effect of a satellite-borne SAR is characterized by comprising the following steps:
obtaining a satellite-borne SAR two-dimensional echo model based on a Doppler frequency shift quantity with azimuth time as a variable;
respectively carrying out distance direction Fourier transform and azimuth direction Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance direction and azimuth direction two-dimensional frequency domain echo model;
obtaining a Doppler frequency shift compensation function based on a Doppler frequency shift term in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction;
and acquiring echo data, and performing range pulse compression on the echo data based on the Doppler frequency shift compensation function.
2. The two-dimensional compensation method for the intra-pulse Doppler effect of the spaceborne SAR according to claim 1, wherein the two-dimensional echo model of the spaceborne SAR is as follows:
wherein the first phase termIs a frequency shift portion; a. the0is a constant, t is the distance direction fast time, η is the azimuth direction slow time, ηcfor the beam center time, c is the propagation velocity of the transmit signal, λ is the wavelength of the transmit signal, φ (-) is the time domain phase of the transmit signal, R (η) is the target slope distance varying along the azimuth time, R' (η) is the first derivative of R (η), wr(. is a distance-to-time envelope, wa(. cndot.) is the azimuth time envelope.
3. The two-dimensional compensation method for the Doppler effect in the satellite-borne SAR pulse according to claim 1, wherein the two-dimensional frequency domain echo models in the distance direction and the azimuth direction are as follows:
wherein f isηIs the azimuth frequency, Wa(fη) Is the azimuthal spectral envelope. Thetaa(ft,fη) Comprises the following steps:
wherein, VSIs the speed of the platform of the spaceborne SAR.
4. The two-dimensional compensation method for the Doppler effect in the satellite-borne SAR pulse according to claim 1, wherein the Doppler shift compensation function is as follows:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*
wherein FTt(. cndot.) is a distance-to-Fourier transform.
5. A two-dimensional compensation device for the intra-pulse doppler effect of a space-borne SAR, the device comprising:
the echo model building unit is used for obtaining a satellite-borne SAR two-dimensional echo model based on the Doppler frequency shift quantity taking azimuth time as a variable;
the Fourier transform unit is used for respectively carrying out distance Fourier transform and azimuth Fourier transform on the satellite-borne SAR two-dimensional echo model to obtain a distance-direction and azimuth-direction two-dimensional frequency domain echo model;
the compensation function building unit is used for obtaining a Doppler frequency shift compensation function based on Doppler frequency shift terms in the two-dimensional frequency domain echo model in the distance direction and the azimuth direction;
an acquisition unit for acquiring echo data;
and the range pulse compression unit is used for performing range pulse compression on the echo data based on the Doppler frequency shift compensation function.
6. The two-dimensional compensation device for the intra-pulse Doppler effect of the spaceborne SAR according to claim 5, wherein the two-dimensional echo model of the spaceborne SAR is as follows:
wherein the first phase termIs a frequency shift portion; a. the0is a constant, t is the distance direction fast time, η is the azimuth direction slow time, ηcfor the beam center time, c is the propagation velocity of the transmit signal, λ is the wavelength of the transmit signal, φ (-) is the time domain phase of the transmit signal, R (η) is the target slope distance varying along the azimuth time, R' (η) is the first derivative of R (η), wr(. is a distance-to-time envelope, wa(. cndot.) is the azimuth time envelope.
7. The two-dimensional compensation device for the Doppler effect in the satellite-borne SAR pulse according to claim 5, wherein the two-dimensional frequency domain echo models in the distance direction and the azimuth direction are as follows:
wherein f isηIs the azimuth frequency, Wa(fη) Is the azimuthal spectral envelope. Thetaa(ft,fη) Comprises the following steps:
wherein, VSIs the speed of the platform of the spaceborne SAR.
8. The two-dimensional compensation device for the Doppler effect in the satellite-borne SAR pulse according to claim 5, wherein the Doppler shift compensation function is as follows:
Hcom(ft,fη)={FTt[s(t)·exp(j2πfηt)]}*
wherein FTt(. cndot.) is a distance-to-Fourier transform.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 4.
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